Exhibit 99.1

NEWS RELEASE

FOR IMMEDIATE RELEASE

CENTURY BANCORP, INC. ANNOUNCES INCREASED YEAR-TO-DATE EARNINGS FOR 2013, UP 5%; ASSET GROWTH OF 8.9% TO RECORD SIZE OF $3.4 BB; REGULAR DIVIDEND DECLARED

Medford, MA, October 8, 2013—Century Bancorp, Inc. (NASDAQ:CNBKA) (www.centurybank.com) (“the Company”) today announced net income of $15,021,000 for the nine months ended September 30, 2013, or $2.70 per Class A share diluted, an increase of 5.3% compared to net income of $14,261,000, or $2.57 per Class A share diluted, for the same period a year ago. Total assets increased 8.9% from $3.1 billion at December 31, 2012 to $3.4 billion at September 30, 2013. For the quarter ended September 30, 2013, net income totaled $5,519,000, or $0.99 per Class A share diluted, a decrease of 2.9% compared to net income of $5,682,000, or $1.02 per Class A share diluted, for the same period a year ago. The decrease in net income was primarily attributable to a decrease in prepayment penalties collected during the quarter ended September 30, 2013 compared to the same period last year.

Net interest income totaled $44.9 million for the nine months ended September 30, 2013 compared to $47.0 million for the same period in 2012. The 4.6% decrease in net interest income for the period is primarily due to $3.0 million of prepayment penalties collected during the first nine months of 2012 compared to $424,000 for the first nine months of 2013. The net interest margin decreased from 2.58% on a fully taxable equivalent basis in 2012 to 2.21% on the same basis for 2013. This was primarily the result of a decrease in asset yields. Also, interest expense decreased primarily as a result of the continued decline in market rates and there was a 13.6% increase in the average balances of earning assets, combined with a similar increase in average deposits.

The provision for loan losses decreased by $1.0 million from $3.3 million for the nine months ended September 30, 2012 to $2.3 million for the nine months ended September 30, 2013, primarily as a result of a lower level of charge-off activity and changes in portfolio composition. The Company capitalized on favorable market conditions for the first nine months ended September 30, 2013 and realized net gains on sales of investments of $2.7 million, as compared to $1.1 million for the same period in 2012. The Company’s effective tax rate decreased from 8.1% in 2012 to 5.6% in 2013 primarily as a result of an increase in tax-exempt income.

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At September 30, 2013, total equity was $166.3 million compared to $180.0 million at December 31, 2012. The Company’s equity decreased primarily as a result of an increase in other comprehensive loss, net of taxes, and dividends paid, offset somewhat by earnings. Other comprehensive loss, net of taxes, increased as a result of an increase in unrealized losses on securities available-for-sale and securities transferred from available-for-sale to held-to-maturity. Unrealized losses increased as a result of increases in interest rates. 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 6.54% at September 30, 2013, compared to 6.80% at December 31, 2012. The decrease in the leverage ratio is due to an increase in assets. Book value as of September 30, 2013 was $29.93 per share compared to $32.40 at December 31, 2012.

The Company’s allowance for loan losses was $21.3 million or 1.73% of loans outstanding at September 30, 2013, compared to $19.2 million or 1.73% of loans outstanding at December 31, 2012 and $18.7 million or 1.75% of loans outstanding at September 30, 2012. The increase in the allowance for loan losses was due to the increase in the size and composition of the loan portfolio as well as qualitative factors. Non-performing assets totaled $3.7 million at September 30, 2013, compared to $4.5 million at December 31, 2012 and $5.9 million at September 30, 2012.

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 15, 2013 to stockholders of record on November 1, 2013.

The Company, through its subsidiary bank, Century Bank and Trust Company, a state chartered full service commercial bank, operating twenty-five 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 Nine months ended September 30, 2013 and 2012

(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)