Robert R. Fears (1830–1914) was an American politician who served as the first Mayor of Gloucester, Massachusetts.

As a young man he worked in the sail making business with his father and was a member of the state militia.

One February 20, 1873, a special town meeting voted 394 to 48 to petition the Massachusetts General Court for a city charter.

[2] Gloucester switched to a city form of government in 1874 and Fears ran for mayor.

He was the president of the Cape Ann Savings Bank for 25 years and a director of the Gloucester Safe Deposit and Trust Company.