Allied Irish Bank has admitted overcharging customers by around €14m over a number of years.
In a statement AIB said it is embarrassed by this revelation and is extremely sorry.
It is believed those affected have been foreign exchange customers.
The bank has also said it will be impossible to identify all the cases but are in discussions with the Financial Services Regulatory Authority about how best to deal with the problem.
Dermot Jewell of the Consumers Association of Ireland has said: "It's a bad situation and it reflects very badly on the systems that operate within the bank."