The incident happened at the Bank of Scotland in Dumbarton Road in the Scotstoun area of Glasgow at about 3.35pm yesterday.
A man who appeared to have a firearm left empty-handed after he entered the bank, threatened a female staff member and demanded money.
The suspect is described as white, in his late 30s to 40s and slim with a gaunt appearance and a Scottish accent.
At the time he was wearing a black, shoulder-length wig, a white baseball cap, a tweed suit jacket, red tartan scarf and blue jeans.
Detective Constable Alister Thom, from the robbery unit at Pollok, Glasgow, appealed for witnesses.
He said: "At this time we are examining CCTV in an effort to identify the person responsible.
"It is believed that he may have been in the area of Harland Street near to the bank before he entered the premises.
"He also headed off in that general direction and was last seen in Harland street at Gleneagles Lane.
"Dumbarton Road is always busy with traffic and pedestrians, and I am sure that people would have seen him in the area.
"His clothing, together with the wig, would have made him quite distinctive and I would urge anyone who saw him to come forward."
Anyone with information is asked to contact police on 101 or Crimestoppers on 0800 555 111.