UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 8-K

CURRENT REPORT

Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934

Date of Report (Date of earliest event reported): May 16, 2013

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions:

Item 8.01 Other Events.

Effective May 16, 2013, United Development Funding III, L.P. (“UDF III” or the “Registrant”) has announced the following changes to its Unit Redemption Program:

An estate, heir or beneficiary that wishes to have units redeemed following the death of a limited partner must mail or deliver a written request on a form provided by UDF III, including evidence acceptable to UDF III’s general partner of the death of the limited partner, and executed by the executor or executrix of the estate, the heir or beneficiary, or their trustee or authorized agent. Limited partners that elect redemption because of an involuntary exigent circumstance must submit proper documentation substantiating their claim for review and approval by UDF III’s general partner in order to be included in the exigent circumstances category.

UDF III’s general partner will determine from time to time whether UDF III has sufficient excess funds from operations to redeem units. Once an amount has been allocated for redemption, the pending redemption requests will be honored among all requesting limited partners in any given redemption period, as follows: first, pro rata as to redemptions upon the death of a limited partner, then pro rata as to redemptions to limited partners who have demonstrated involuntary exigent circumstances. Any and all units not redeemed may be withdrawn at the election of the limited partner. Any units not withdrawn will remain pending redemption and will be reviewed at such time as UDF III’s general partner allocates additional funds for redemption.

The purchase price for the units redeemed because of involuntary exigent circumstances, for the period beginning after a limited partner has held the units for a period of one year, will be (1) 92% of the purchase price actually paid for any units held less than two years, (2) 94% of the purchase price actually paid for any units held for at least two years but less than three years, (3) 96% of the purchase price actually paid for any units held at least three years but less than four years, (4) 98% of the purchase price actually paid for any units held at least four years but less than five years and (5) the lesser of the purchase price actually paid for any units held at least five years or the then-current fair market value of the units as determined by the most recent valuation of the units (as of May 16, 2013, the most recent valuation of the units is $20 per unit). The purchase price for units redeemed upon the death of a limited partner will be the lesser of (1) the price the limited partner actually paid for the units or (2) the then-current fair market value of the units as determined by the most recent valuation of the units. The purchase price for any redeemed units will be offset by any net proceeds from capital transactions previously distributed to the limited partner, or his or her estate, in respect of such units as a return of capital contributions. Once a limited partner’s outstanding units have been redeemed, the investor is no longer considered a limited partner.

UDF III will not redeem in excess of 5% of the weighted average number of units outstanding during the twelve-month period immediately prior to the date of redemption. Generally, the cash available for redemption will be limited to 1% of the operating cash flow from the previous fiscal year, plus any proceeds from UDF III’s distribution reinvestment plan.

UDF III’s general partner, in its sole discretion, may choose to terminate or suspend the Unit Redemption Program at any time it determines that such termination or suspension is in the best interest of the Registrant or it determines that the funds otherwise available to fund the Unit Redemption Plan are needed for other purposes. UDF III’s general partner also maintains the right in its sole discretion at any time and from time to time to reject any request for redemption. Except as provided herein, the remaining terms and conditions of the Unit Redemption Program shall remain in full force and effect.

SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the Registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.