Barclays Bank is set to offer a new one-to-one video service to some customers from 8 December - what it says is a first for UK banking.
Video banking will allow premier account customers to speak securely to bank staff at any time of the day.
The service will mean customers can communicate with employees from their mobile phone, tablet or laptop.
Steven Cooper, CEO of personal banking at Barclays, said it would be a "watershed moment" in UK banking.
He said it would mean banks "interact with customers completely on their terms, rather than ours".
The service will be rolled out to mortgage, business and wealth customers from early 2015.
It will then be made available to all retail customers.
Where possible, customers will be connected to a staff member they have already spoken to.
Mr Cooper added: "While many of our customers are increasingly using digital channels to complete routine transactions, for the important moments, you just can't beat face-to-face conversations, yet traditional branch opening hours don't always give customers that choice."