The parent company of Scottish Gas reported profits from residential energy supply were up 11% last year on 2011. It also said gas consumption rose 12%.
In November, the company raised its gas and electricity prices by 6% for around 8.4 million households.
The profits surge was condemned by campaign groups but bosses defended the results, adding that the firm had made just under £50 profit per customer household.
Centrica chief executive Sam Laidlaw said its profit margins per household "actually went down".
But the figures were slammed by charity Age Scotland. A spokesman said: "Over half of single pensioner households in Scotland are in fuel poverty.
"So these profit figures are unlikely to be well-received by older customers who faced a stark choice this winter between heating and eating."
Tom Greatrex MP, shadow energy minister, said the results show it is time for a "complete overhaul of our energy market".
He added: "People will not understand why just a few months ago Scottish Gas claimed they had no option but to put up their prices when now it looks like they are making huge profits on the back of spiralling bills for hard-pressed consumers.
"It is unacceptable that David Cameron is letting the energy companies get away with inflation-busting price rises when they are already making huge profits and when people can least afford it."
Consumer chiefs said the results raise questions over the fairness of price rises.
Richard Lloyd, executive director of Which?, said: "People are bound to question whether they're paying a fair price for energy when they see big profits announcements.
"Centrica's analysis won't change that view as record-high bills land on millions of doormats."
Profits were up 16% to £312m at Centrica's residential services unit, which covers services such as boiler repairs.
Centrica, also British Gas's parent firm, reported adjusted operating profit of £2.7bn for 2012, up 14% from 2011.
The company said it paid more than £1bn in tax and invested £2.7bn last year.
Chris Jansen, managing director of services and commercial at Centrica, said: "It's important to remember that in 2011 it was a very, very mild winter ... so the country used a lot less gas, and actually our profits in 2011 were 20% down on 2010."