The company's tariffs were not explained clearly to customers
The energy supplier Npower has been told to repay £1.2m to 200,000 of its gas customers.
The regulator Ofgem said they had paid more than expected when their gas tariffs were changed by the company in the course of 2007.
Ofgem said many customers benefitted, but those households which did not use much gas were made worse off.
An Npower spokesman said refunds were "the right thing to do" and letters would be sent to those affected.
Those who are still with Npower will receive a credit on their next bill while former customers will be sent a refund, Npower said.
Ofgem said the problem arose with the application of Npower's two-tier tariffs - the standard arrangement in the energy industry.
Under these the first chunk of gas consumption is charged at a higher level than subsequent usage.
A spokesman for the regulator said that when the company cut its overall level of charges, it did make clear to customers that some of them might simultaneously be moved from its new lower level tariff back to the higher one.
"The amount of gas consumed during the tariff year that is subject to the higher charge varies according to season," said the regulator.
"Every time Npower altered its charges it started a new tariff year on which charges are based.
"So some consumers whose consumption had taken them into the lower level charges were placed back on the higher level when new charges were introduced," it added.
The issue was first highlighted in the pages of the Guardian newspaper by a reader, Robert Bramwell, who was then featured on the BBC Watchdog programme.
The retired art teacher found that he could not understand the charges that had been applied to his bills.
He spent 18 months badgering Npower and trying to convince it that it had overcharged him, and possibly many others, before his complaints were taken seriously, leading Ofgem to investigate in June 2008.
At the time it was alleged that the company might have overcharged more than two million customers by about £60m, something it strenuously denied.