EXHIBIT 99.1

Mid-Con Energy Partners, LP Announces First Quarter 2013 Results

DALLAS, May 7, 2013 – Mid-Con Energy Partners, LP (NASDAQ: MCEP) (“Mid-Con Energy” or the “Partnership”) announced today its financial and operating results for the first quarter ended March 31, 2013.

Mid-Con Energy highlighted the following achievements for the first quarter of 2013:

The following table reflects selected operating and financial results for the first quarter of 2013, compared to the first quarter of 2012 and fourth quarter of 2012. Mid-Con Energy’s consolidated financial statements can be found in the supplemental tables of this press release.

Randy Olmstead, Chief Executive Officer, commented, “The positive momentum established by our team during 2012 has clearly carried over into the first quarter of 2013. Mid-Con Energy’s continued growth in oil production further validates our ability to exploit the organic potential of our existing asset base and acquire properties that fit our waterflood strategy. Correspondingly, the expansion of our Distributable Cash Flow during the first quarter of 2013 translated into tangible success for our unitholders by increasing the quarterly cash distribution rate for the third consecutive quarter.”

First Quarter 2013 Results

Production volumes for the first quarter of 2013 were 226 thousand barrels of oil equivalent (MBoe) or approximately 2,511 Boe per day on average. In comparison, Mid-Con Energy’s production volumes for the first quarter of 2012 were 155 MBoe, or approximately 1,703 Boe per day on average. Year over year gains in production were propelled by continued waterflood response to injection, infill drilling in the Partnership’s Southern Oklahoma core area and the full quarter impact of properties acquired during 2012.

Oil sales, excluding the effect of commodity derivatives, were $20.0 million in first quarter of 2013 and resulted in an average realized oil price of $90.90 per barrel (Bbl), compared to $102.24 per Bbl in the first quarter of 2012. Approximately 81% of Mid-Con Energy’s oil production during the first quarter of 2013 was hedged at an average price of $98.07 per Bbl. Given the favorable variance between the average hedge price and NYMEX WTI, the Partnership received $0.7 million for realized commodity derivatives during the first quarter of 2013, or $3.06 per Bbl. In comparison, Mid-Con Energy paid $0.1 million for realized commodity derivatives during the first quarter of 2012, or ($0.89) per Bbl.

Lease operating expenses were $3.3 million, or $14.81 per Boe, in the first quarter of 2013, compared to $1.9 million, or $12.56 per Boe, in the first quarter of 2012. Total lease operating expenses increased over the prior year period largely due to an expansion in well count stemming from development programs and properties acquired during 2012.

Production taxes in the first quarter of 2013 were $0.8 million, or $3.50 per Boe, for an effective tax rate of approximately 3.9%. Production taxes in the first quarter of 2012 were $0.7 million, or $4.33 per Boe, for an effective tax rate of approximately 4.3%. A portion of Mid-Con Energy’s wells in Oklahoma continue to receive a reduced production tax rate due to the state’s Enhanced Recovery Project Gross Production Tax Exemption.

Total general and administrative expenses during the first quarter of 2013 were $6.7 million and included $4.6 million in non-cash equity-based compensation expense related to the Partnership’s long-term incentive program. Total general and administrative expenses during the first quarter of 2012 were $3.6 million and included $2.7 million in non-cash equity based compensation expense.

Adjusted EBITDA for the first quarter of 2013 was $14.6 million, approximately 24% above Adjusted EBITDA of $11.8 million for the first quarter of 2012. Distributable Cash Flow for the first quarter of 2013 was $12.0 million after subtracting $0.6 million in cash interest expense and $2.0 million in estimated maintenance capital expenditures.

Mid-Con Energy reported net income of $4.1 million, or $0.21 per limited partner unit, for the first quarter of 2013. This included $1.8 million of unrealized losses from commodity derivatives. Net income during the first quarter of 2012 was $1.7 million, or $0.09 per limited partner unit, and included $4.8 million of unrealized losses from commodity derivatives.

Increased Cash Distribution

As announced on April 23, 2013, the Board of Directors of Mid-Con Energy’s general partner declared its third consecutive increase in the quarterly cash distribution rate to $0.505 per unit for the quarter ended March 31, 2013. This represented an approximate 6% increase over the $0.475 per unit rate declared at the Partnership’s initial public offering in December 2011. The cash distribution will be paid May 14, 2013 to unitholders of record at the close of business on May 7, 2013.

Hedging Update

Mid-Con Energy enters into various commodity derivative contracts intended to achieve more predictable cash flows and to reduce its exposure to fluctuations in the price of oil. The Partnership’s hedging program objective is to protect its ability to make current distributions, and to be better positioned to increase its quarterly distribution over time, while retaining some ability to participate in upward movements in oil prices. Mid-Con Energy uses a phased approach, looking approximately 36 months forward while targeting a higher hedged percentage in the near 12 months of the period.

Supplementing its primary hedging strategy described above, Mid-Con Energy also intends to enter into additional commodity derivative contracts in connection with material increases in its estimated production and at times when management believes market conditions or other circumstances suggest that it is prudent to do so, as opposed to entering into commodity derivative contacts at predetermined times or on prescribed terms.

As of May 7, 2013, the following table reflects volumes of Mid-Con Energy’s production covered by commodity derivative contracts, and the average prices at which the production will be hedged:

Liquidity Update

As of March 31, 2013, the Partnership’s total liquidity of $50.9 million included $0.9 million in cash and cash equivalents and $50.0 million of available borrowings under the revolving credit facility.

As announced on April 12, 2013, Mid-Con Energy’s bank group unanimously reaffirmed the Partnership’s $130.0 million borrowing base as part of its regularly scheduled semi-annual redetermination. There were no changes to the interest rate, repayment terms or number of banks in the revolving credit facility. The next scheduled redetermination of the borrowing base will occur on or about October 30, 2013.

Quarterly Report on Form 10-Q

Certain financial results included in this press release and related footnotes will be available in Mid-Con Energy’s March 31, 2013 Quarterly Report on Form 10-Q, which will be filed on or before May 10, 2013.

Earnings Conference Call

As announced on April 23, 2013, Mid-Con Energy’s management will host a conference call on Wednesday, May 8, 2013 at 10:00 a.m. ET (9:00 a.m. CT) to discuss operating and financial results. Interested parties are invited to participate via telephone by dialing 1-877-847-5946 (Conference ID: 53251051) at least five minutes prior to the scheduled start time of the call, or via webcast by clicking on “Events & Presentations” in the investor relations section of the Mid-Con Energy website at www.midconenergypartners.com.

A telephonic replay of the conference call will be available through May 15, 2013 by dialing 1-855-859-2056 (Conference ID: 53251051). Additionally, a webcast archive will be available at www.midconenergypartners.com.

About Mid-Con Energy Partners, LP

Mid-Con Energy is a Delaware limited partnership formed in July 2011 to own, operate, acquire, exploit and develop producing oil and natural gas properties in North America, with a focus on the Mid-Continent region of the United States. Mid-Con Energy’s core areas of operation are located in Southern Oklahoma, Northeastern Oklahoma and parts of Oklahoma and Colorado within the Hugoton Basin.

Forward-Looking Statements

This press release includes “forward-looking statements” — that is, statements related to future, not past, events within meaning of the federal securities laws. Forward-looking statements are based on current expectations and include any statement that does not directly relate to a current or historical fact. In this context, forward-looking statements often address expected future business and financial performance, and often contain words such as “anticipate,” “believe,” “estimate,” “intend,” “expect,” “plan,” “project,” “should,” “goal,” “forecast,” “guidance,” “could,” “may,” “continue,” “might,” “potential,” “scheduled,” or “will” or other similar words. These forward-looking statements involve certain risks and uncertainties and ultimately may not prove to be accurate. Actual results and future events could differ materially from those anticipated in such statements. For further discussion of risks and uncertainties, you should refer to Mid-Con Energy’s filings with the SEC available at www.midconenergypartners.com or www.sec.gov. Mid-Con Energy undertakes no obligation and does not intend to update these forward-looking statements to reflect events or circumstances occurring after this press release. You are cautioned not to place undue reliance on these forward-looking statements, which speak only as of the date of this press release. All forward-looking statements are qualified in their entirety by this cautionary statement and our SEC filings.

These forward–looking statements are subject to a number of risks and uncertainties, many of which are beyond our control, which may include statements about our:

Mid-Con Energy Partners, LP and subsidiaries

Consolidated Balance Sheets (Unaudited)

(in thousands)

Mid-Con Energy Partners, LP and subsidiaries

Consolidated Statements of Operations (Unaudited)

(in thousands, except per unit data)

Mid-Con Energy Partners, LP and subsidiaries

Consolidated Statements of Cash Flows (Unaudited)

(in thousands)

Non-GAAP Financial Measures

This press release, financial tables and other supplemental information include “Adjusted EBITDA” and “Distributable Cash Flow”, each of which are non-generally accepted accounting principles (“Non-GAAP”) measures used by our management to describe financial performance with external users of our financial statements.

The Partnership believes the Non-GAAP financial measures described above are useful to investors because these measurements are used by many companies in its industry as a measurement of financial performance and are commonly employed by financial analysts and others to evaluate the financial performance of the Partnership and to compare the financial performance of the Partnership with the performance of other publicly traded partnerships within its industry.

Adjusted EBITDA and Distributable Cash Flow should not be considered an alternative to net income, net cash provided by operating activities or any other measure of financial performance or liquidity presented in accordance with GAAP.

Adjusted EBITDA is defined as net income (loss)

Plus:

Less:

Distributable Cash Flow is defined as Adjusted EBITDA

Less:

Reconciliation of Net Income to Adjusted EBITDA and Distributable Cash Flow

(in thousands)

CONTACT:

Jeff Olmstead

President and Chief Financial Officer

(972) 479-5980

jolmstead@midcon-energy.com

Matthew Lewis

Associate

(972) 479-5984

mlewis@midcon-energy.com