In three of the robberies, the man held a knife to the throat of bank customers standing at teller windows, injuring a male customer in one case, police said.
The robberies happened March 22 at a Citibank at 1801 Van Ness Ave.; March 24 at an East West Bank at 743 Washington St.; April 2 at a Wells Fargo Bank at 1160 Grant Ave.; and on Monday at a City National Bank at 150 California St, according to police.
The robber used a weapon in all but the March 22 robbery, police said.
A male customer suffered a minor injury in the April 2 robbery, and during Monday's robbery, the suspect held a knife to the throat of a 90-year-old woman, police said. The woman was not hurt.
The robberies were captured on surveillance video at the banks. Police Inspector Phillip Wong said the same man is believed to have robbed all four banks.
He is described as a black man between 30 and 40 years old, about 6 feet tall and 175 pounds, with black hair, a moustache and a goatee. He wore a dark baseball cap in all of the robberies.
Anyone with information about the crimes is asked to call Inspector Wong at (415) 553-1201, the confidential tip line (415) 575-444, or text-a-tip by typing "TIP411" and then "SFPD."