It happened around 9:30 a.m.
Durham Police Department said the robber handed the bank teller a note demanding money and implying that he had a gun. That gun was never seen.
The teller handed over an undisclosed amount of money and the robber ran off down Carver Street.
Police have not released the identity or description of the suspect. Anyone with information about what happened is asked to call CrimeStoppers at 919-683-1200.