Exhibit 99.1

NEWS RELEASE

FOR IMMEDIATE RELEASE

CENTURY BANCORP, INC. ANNOUNCES 5TH CONSECUTIVE YEAR OF RECORD EARNINGS FOR 2014, UP 9%; ASSET GROWTH TO RECORD SIZE OF $3.6 BB; REGULAR DIVIDEND DECLARED

Medford, MA, January 20, 2015—Century Bancorp, Inc. (NASDAQ:CNBKA) (www.centurybank.com) (“the Company”) today announced net income of $21,860,000 for the year ended December 31, 2014, or $3.93 per Class A share diluted, an increase of 9.0% compared to net income of $20,046,000, or $3.61 per Class A share diluted, for the same period a year ago. Total assets increased 5.6% from $3.4 billion at December 31, 2013 to $3.6 billion at December 31, 2014. For the quarter ended December 31, 2014, net income totaled $5,623,000 or $1.01 per Class A share diluted, an increase of 11.9% compared to net income of $5,025,000, or $0.90 per Class A share diluted, for the same period a year ago.

Net interest income totaled $66.2 million for the year ended December 31, 2014 compared to $61.0 million for the same period in 2013. The 8.7% increase in net interest income for the period is primarily due to an increase in average earning assets. The net interest margin increased from 2.21% on a fully taxable equivalent basis in 2013 to 2.22% on the same basis for 2014. This was primarily the result of a decrease in rates paid on deposits and borrowed funds. Also, interest expense increased slightly as a result of an increase in deposit balances and there was a 8.5% increase in the average balances of earning assets, combined with a similar increase in average deposits.

The provision for loan losses decreased by $660,000 from $2.7 million for the year ended December 31, 2013 to $2.1 million for the same period in 2014, primarily as a result of changes in the portfolio composition and changes in qualitative economic factors. The Company capitalized on favorable market conditions for the year ended December 31, 2014 and realized net gains on sales of investments of $450,000, as compared to $3.0 million for the same period in 2013. The Company’s effective tax rate decreased from 4.8% in 2013 to 3.8% in 2014 primarily as a result of an increase in tax-exempt income.

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At December 31, 2014, total equity was $192.5 million compared to $176.5 million at December 31, 2013. The Company’s equity increased primarily as a result of earnings, offset somewhat by an increase in other comprehensive loss, net of taxes, and dividends paid. Other comprehensive loss, net of taxes, increased as a result of an increase in the additional pension liability. The pension liability increased as a result of an increase in the discount rate utilized and the impact of recently updated mortality tables. This was offset somewhat by a decrease in unrealized losses on securities available-for-sale and securities transferred from available-for-sale to held-to-maturity. 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.

The Company’s leverage ratio stood at 6.91% at December 31, 2014, compared to 6.50% at December 31, 2013. The increase in the leverage ratio was due to an increase in stockholders’ equity, offset somewhat by an increase in quarterly average assets. Book value as of December 31, 2014 was $34.57 per share compared to $31.76 at December 31, 2013.

The Company’s allowance for loan losses was $22.3 million or 1.68% of loans outstanding at December 31, 2014, compared to $20.9 million or 1.66% of loans outstanding at December 31, 2013. The increase in the allowance for loan losses was due to the increase in the size of the loan portfolio. Non-performing assets totaled $4.1 million at December 31, 2014, compared to $2.5 million at December 31, 2013.

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 February 17, 2015 to stockholders of record on February 2, 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 and Year ended December 31, 2014 and 2013

(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)