He made off with the cash from the Royal Bank of Scotland in Edinburgh's St John's Road after threatening a member of staff at around 9.30am.
He walked up to the counter and demanded money before fleeing with a four-figure sum in an orange Tesco carrier bag.
The suspect was last seen getting into a black cab which headed west.
Detective Inspector Rory Hamilton appealed for witnesses to come forward.
He said: "At no time was any weapon used or seen by staff or customers within the bank. However, the suspect was still able to make off with thousands of pounds and we are keen to hear from anyone who can help us in tracing this individual.
"We believe the male may have arrived and departed from the scene in the same black cab and we are in the process of speaking to the city's taxi companies as part of our investigation. Any drivers who believe they may have taken this man to and from the bank is also asked to get in touch."
The man is white, aged in his late 20s to early 30s and 6ft 4in. He was wearing a black beanie hat, a dark waist-length jacket and brown trousers.
Anyone with information can contact Police Scotland on 101 or Crimestoppers on 0800 555 111.