The woman, from Crocketford in Dumfries and Galloway, was phoned at home by someone claiming to be from Royal Bank of Scotland, and was told that someone tried to withdraw £5,000 from her account, police said.
She was asked to confirm her bank details and when she refused, the caller told her to phone the bank herself and confirm that the call was genuine.
But the original caller did not hang up, meaning that when the woman dialled for the bank she was still connected to the scam call, Dumfries and Galloway Police said.
"The phone was answered by someone who said 'Royal Bank of Scotland', thus indicating to the woman that she had got through to her bank," a police spokesman said.
"It now transpires that nearly £20,000 has been taken from her account by fraudulent means. It seems that the original caller to the woman did not hang up the phone after the call and so was able to pretend to be from the bank when the woman made the call to the bank."
The public are being urged to be aware of the scam and asked anyone with any information on the theft to call them on 08456 005 701 or anonymously via Crimestoppers on 0800 555 111.