The Wells Fargo at 4765 Hopyard Road was robbed at about 11:10 a.m., police said.
The man approached a teller with a note that said he was robbing the bank.
The suspect ran away with cash stolen from the bank. Witnesses did not see the man with a weapon or a vehicle, police said.
He is described as a black man between 30 and 40 years old, standing between 5 feet 10 inches and 6 feet tall, weighing between 160 and 175 pounds with black hair, brown eyes and a goatee.
During the robbery he was wearing a light colored long-sleeve shirt, blue or gray pants and sunglasses. He spoke with a Jamaican or similar accent.
Anyone who has seen the man has been asked to call Pleasanton police at (925) 931-5100.