The “fraud refund guarantee” will cover cases where customers are tricked into authorising payments to fraudsters, as well as unauthorised transactions.
The move comes as the bank tries to rebuild its image after an IT meltdown last April left 1.9 million customers unable to access their own money.
Banks have been under pressure to help tackle the rise in sophisticated fraud.
Some £354m was lost last year through this type of scam, known as a “push” or “authorised” payment fraud, according to banking trade body UK Finance.
Financial firms returned just £83m of this to customers.