Exhibit 99.1

NEWS RELEASE

FOR IMMEDIATE RELEASE

CENTURY BANCORP, INC. ANNOUNCES EARNINGS FOR Q3 2015, UP 8.1%; LOAN

GROWTH OF 23%; ASSET GROWTH TO $3.9 BB; REGULAR DIVIDEND DECLARED

Medford, MA, October 13, 2015—Century Bancorp, Inc. (NASDAQ:CNBKA) (www.centurybank.com) (“the Company”) today announced record net income of $17,050,000 for the nine months ended September 30, 2015, or $3.06 per Class A share diluted, an increase of 5.0% compared to net income of $16,237,000, or $2.92 per Class A share diluted, for the same period a year ago. Total assets increased 6.4% from $3.6 billion at December 31, 2014 to $3.9 billion at September 30, 2015. For the quarter ended September 30, 2015, net income totaled $6,166,000 or $1.11 per Class A share diluted, an increase of 8.1% compared to net income of $5,706,000, or $1.03 per Class A share diluted, for the same period a year ago.

Net interest income totaled $52.7 million for the nine months ended September 30, 2015 compared to $50.0 million for the same period in 2014. The 5.4% increase in net interest income for the period is primarily due to an increase in average earning assets. The net interest margin decreased from 2.23% on a fully taxable equivalent basis in 2014 to 2.20% on the same basis for 2015. This was primarily the result of a decrease in rates on earning assets. The average balances of earning assets increased by 7.6% combined with a similar increase in average deposits. Also, interest expense increased 3.9% as a result of an increase in deposit balances.

The provision for loan losses decreased by $1,450,000 from $1,650,000 for the nine months ended September 30, 2014 to $200,000 for the same period in 2015, primarily as a result of changes in portfolio composition. The Company’s effective tax rate decreased from 4.4% in 2014 to 3.6% in 2015 primarily as a result of an increase in tax-exempt income.

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At September 30, 2015, total equity was $211.1 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 primarily as a result of a decrease in unrealized losses on 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.

The Company’s leverage ratio stood at 6.71% at September 30, 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 September 30, 2015 was $37.92 per share compared to $34.57 at December 31, 2014.

The Company’s allowance for loan losses was $22.3 million or 1.36% of loans outstanding at September 30, 2015, compared to $22.3 million or 1.68% of loans outstanding at December 31, 2014 and $22.5 million or 1.66% of loans outstanding at September 30, 2014. The change in the ratio of the allowance for loan losses to loans outstanding was primarily due to changes in portfolio composition. Non-performing assets totaled $1.8 million at September 30, 2015, compared to $4.1 million at December 31, 2014 and $6.0 million at September 30, 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 November 16, 2015 to stockholders of record on November 2, 2015.

The Company, through its subsidiary bank, Century Bank and Trust Company, a state chartered full service commercial bank, operating twenty-seven 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.