It happened at about noon in the 4300 block of Bells Ferry Road.
Police said the robber entered the bank and demanded money from a teller. They said he fled on foot with an undisclosed amount of cash.
SLIDESHOW: Robber Wearing Cowboy Hat Hits Cobb Bank
The robber was last seen running into a wooded area behind the bank and a nearby QuikTrip gas station.
Authorities described the robber as a white man, 20-24 years old, 6 feet tall with a slim build. Authorities said he was clean shaven. He was last seen wearing a light-colored blazer, a white sweater, a light-colored cowboy hat, gloves and sunglasses.