Detectives are investigating after the attempted armed robbery was reported on Wednesday night.
The incident happened at a bookies on the Falls Road shortly before 9.30pm.
The man, who is described as being about 5ft 9ins tall, made his demands for money but ended up making off on foot when he was refused.
He is said to have been wearing a hooded top, blue jeans, white trainers and a scarf which covered his face at the time of the incident.
Police are asking anyone with information to contact them at Grosvenor Road.