Exhibit 99.1

NEWS RELEASE

FOR IMMEDIATE RELEASE

CENTURY BANCORP, INC. ANNOUNCES EARNINGS FOR Q1 2015, UP 0.5%; ASSET

GROWTH TO RECORD SIZE OF $3.8 BB; REGULAR DIVIDEND DECLARED

Medford, MA, April 14, 2015—Century Bancorp, Inc. (NASDAQ:CNBKA) (www.centurybank.com) (“the Company”) today announced net income of $4,959,000 for the quarter ended March 31, 2015, or $0.89 per Class A share diluted, an increase of 0.5% compared to net income of $4,932,000, or $0.89 per Class A share diluted, for the same period a year ago. Total assets increased 4.1% from $3.6 billion at December 31, 2014 to $3.8 billion at March 31, 2015. Earnings are up slightly compared to the same period last year; however, the harsh winter caused increased expenses and lower revenues during the first quarter of 2015 compared to the same period a year ago.

Net interest income totaled $16.4 million for the quarter ended March 31, 2015 compared to $16.5 million for the same period in 2014. The 0.6% decrease in net interest income for the period is primarily due to a decrease in the net interest margin. The net interest margin decreased from 2.27% on a fully taxable equivalent basis in 2014 to 2.12% on the same basis for 2015. This was primarily the result of a decrease in rates on earning assets. Also, interest expense increased slightly as a result of an increase in deposit balances and there was a 7.8% increase in the average balances of earning assets, combined with a similar increase in average deposits.

The provision for loan losses decreased by $400,000 from $600,000 for the quarter ended March 31, 2014 to $200,000 for the same period in 2015, primarily as a result of stable loan balances and low charge-off levels. The Company’s effective tax rate decreased from 5.6% in 2014 to 4.2% in 2015 primarily as a result of an increase in tax-exempt income.

At March 31, 2015, total equity was $197.8 million compared to $192.5 million at December 31, 2014. The Company’s equity increased primarily as a result of earnings and a decrease in other comprehensive loss, net of taxes, offset somewhat by dividends paid. Other comprehensive loss, net of taxes, decreased as a result of a decrease in unrealized losses on securities available-for-sale and securities transferred from available-for-sale to held-to-maturity and amortization of the pension liability. During the third quarter of 2013, $987.0 million of securities available-for-sale with unrealized losses of $25.3 million were transferred to securities held-to-maturity. This was done in response to rising interest rates.

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The Company’s leverage ratio stood at 6.60% at March 31, 2015, compared to 6.91% at December 31, 2014. The decrease in the leverage ratio was due to an increase in quarterly average assets, offset somewhat by an increase in stockholders’ equity. Book value as of March 31, 2015 was $35.53 per share compared to $34.57 at December 31, 2014.

The Company’s allowance for loan losses was $22.5 million or 1.68% of loans outstanding at March 31, 2015, compared to $22.3 million or 1.68% of loans outstanding at December 31, 2014 and $21.3 million or 1.68% of loans outstanding at March 31, 2014. The increase in the allowance for loan losses was due to the increase in the size of the loan portfolio. Non-performing assets totaled $4.3 million at March 31, 2015, compared to $4.1 million at December 31, 2014 and $1.6 million at March 31, 2014.

The Company’s Board of Directors voted a regular quarterly dividend of 12.00 cents ($0.12) per share on the Company’s Class A common stock, and 6.00 cents ($0.06) per share on the Company’s Class B common stock. The dividends were declared payable May 15, 2015 to stockholders of record on May 1, 2015.

The Company, through its subsidiary bank, Century Bank and Trust Company, a state chartered full service commercial bank, operating twenty-six full-service branches in the Greater Boston area, offers a full range of Business, Personal and Institutional Services.

Century Bank and Trust Company is a member of the FDIC and is an Equal Housing Lender.

This press release contains certain “forward-looking statements” with respect to the financial condition, results of operations and business of the Company. Actual results may differ from those contemplated by these statements. The Company wishes to caution readers not to place undue reliance on any forward-looking statements. The Company disclaims any intent or obligation to update publicly any such forward-looking statements, whether in response to new information, future events or otherwise.

Century Bancorp, Inc. and Subsidiaries

Consolidated Comparative Statements of Condition (unaudited)

(in thousands)

Century Bancorp, Inc. and Subsidiaries

Consolidated Comparative Statements of Income (unaudited)

For the Quarter ended March 31, 2015 and 2014

(in thousands)

Century Bancorp, Inc. and Subsidiaries

Consolidated Year-to-Date Average Comparative Statements of Condition (unaudited)

(in thousands)

Century Bancorp, Inc. and Subsidiaries

Consolidated Selected Key Financial Information (unaudited)

(in thousands, except share data)