The complaint handling regulations took effect from October 2008 and set out the service that domestic and micro-business energy customers should expect from energy companies if they raise a complaint.
Ofgem said an investigation found British Gas failed to re-open unresolved complaints, did not give customers with unresolved complaints key details about redress services provided by the Energy Ombudsman and failed to put in place adequate processes for dealing with complaints from micro-businesses.
The regulator added that British Gas has taken action to improve its complaint handling systems and ensure compliance with Ofgem regulations since the investigation began in June last year.
Wednesday's fine comes barely a month after the regulator said it would fine British Gas 1 million pounds for misreporting the amount of electricity it supplied under the renewables obligation.
Ofgem said it is currently investigating RWE's npower and EDF Energy for complaint handling, and Iberdrola's Scottish Power, Scottish and Southern Energy, EDF Energy and npower for misselling.
The regulator is also undertaking two investigations into Scottish Power for potentially misleading marketing and the difference between its standard credit and direct debit tariffs.