Chief executive Sam Laidlaw took the decision some weeks ago, but only disclosed the news when questioned at the annual conference of the CBI business group in London.
Quizzed about bonus payments during a panel discussion entitled Business Trust Under the Spotlight, he said: "I have already decided to turn down my bonus."
His base pay was £950,000 last year, but with other payments his total package was just under £5 million.
There are two bonus elements, an annual incentive scheme and a long-term incentive scheme.
It is understood his announcement relates to the annual scheme, which pays an average of 180% of his base pay, which is estimated to be worth just over £1.7 million.
Mr Laidlaw told the CBI that trust in the energy sector is at an "all time low", with an urgent need to rebuild it with consumers.
There was a need for leadership in the current environment, he said, adding it had to be balanced with being able to attract employees.
A spokesman for Centrica said: "This is a personal decision, and one he made some weeks ago."
Any further discussions about the pay of Centrica directors will be made by the company's remuneration committee.
Mr Laidlaw repeated the industry's pledge to cut bills if the Government switches environment and social costs to other forms of taxation.
He said the energy industry was "in the eye of the storm", conceding that firms should be more transparent, explain how bills are made up and improve the process of switching suppliers.
Mr Laidlaw said he was focused on helping customers struggling to pay bills this winter.
More than half a million British Gas customers will receive a special discount of £60 this winter, on top of a £135 warm home discount, he said.
Mr Laidlaw said his company had reduced its costs by £300 million over the past few years, and would immediately pass on any reductions in the social and environmental part of energy bills.
"We are listening - we get it, absolutely. We know there is a problem."
Mr Laidlaw said there was no scope for switching profits from one part of the business to another.
Paul Kenny, general secretary of the GMB union, which represents workers at British Gas, said: "It is a treat to welcome the head of a major corporation who is in touch with the public mood.
"It is to be hoped that Mr Laidlaw has started a trend that will be followed quickly by a substantial number of senior executives at other companies across the UK."