Department of Energy and Climate Change (DEDD) personnel booked seats between London and Aberdeen, where its North Sea inspectors work. Flights from London to Manchester and Glasgow and between Aberdeen and Norwich, Southampton and Humberside were also recorded.
The TaxPayers' Alliance found some flights were taken in business class, with one £460 flight from Aberdeen to London, and two Manchester to London flights at £188 each.
Since May 2010, the post of energy secretary has been filled by the Liberal Democrats, who want higher taxes on domestic flights "for which alternative, less polluting travel is readily available".
Matthew Sinclair, of the TaxPayers' Alliance, said: "Despite being one of the departments making air travel more expensive for people paying their own way, the Department of Energy and Climate Change has spent an astonishing amount of taxpayers' money. This looks like breathtaking hypocrisy.
"Officials urgently need to explain why they spend so much money on so many business class flights in particular."
The most expensive of the 3496 flights taken over the last two-and-a-half years was a business class booking from Cancun to London following an international climate change conference. Business class tickets were booked for 362 trips at a cost of nearly £600,000.
A DECC spokesman said: "The department's international work, which includes securing the nation's future energy supplies, carrying out negotiations with other countries and international organisations on energy issues, and regulating the North Sea oil and gas industry among other things, means that sometimes air travel is unavoidable."
It said they were careful to ensure the trips were cost-effective.