TSB has launched a "fraud refund guarantee" that will see all victims of any fraud get their money back.
Becoming the first UK bank to offer such a pledge, TSB said it will cover situations where customers have been tricked into moving money out of their account and unauthorised payments.
Fraudsters have become increasingly sophisticated in tricking unknowing customers in recent years, often able to mimic their customers' banks, even to the point of calling from the banks' phone numbers. Typically banks only refund or recover the money if it is still in the initial bank account.
The move is considered to be a move to entice customers back to TSB, which lost thousands of customers after nearly two million customers were unable to access their accounts in April 2018.
Acting chief executive Richard Meddings said the fraud refund guarantee is "about giving piece of mind to our customers and doing the right thing".
"It's a major societal blight. Innocent customers are being tricked."
In a warning to fraudsters, Mr Meddings said: "If you come for one of my customers, we will hunt you down."
Figures show that £354m was lost to fraud last year but just £83m was returned to customers.
The TSB acting chief executive said: "The vast majority of fraud claims across UK banking are from innocent victims of fraud who have been targeted by criminals and organised gangs.
"However, all too often these customers must fight to be refunded and are not treated as victims of crime."