Chris Finlayson cited personal reasons for his departure, which came three days before the company is due to present first quarter figures.
BG's shares have fallen in recent weeks after it slashed production targets due to continued problems in Egypt, where too much of its gas has been diverted into the domestic market instead of being exported.
Mr Finlayson took on the role from Sir Frank Chapman, who had been in charge since BG was created in 1997 when British Gas demerged into two separately listed companies.
BG said chairman Andrew Gould will take the helm on an interim basis as the company begins the search for an external successor.
Mr Gould said the board remained fully committed to the group's strategy based around a portfolio of "high-quality" assets.
He added: "The company must accelerate the creation and delivery of the longer-term value for our shareholders, while delivering the group's business plans.
"The board felt that it was in the best interests of the group to accept Chris's resignation and seek fresh leadership to deliver both of these priorities."
Mr Finlayson has more than 35 years experience in the oil and gas industry, having joined BG from Royal Dutch Shell in 2010. He was previously in charge of BG's capital projects programme.
BG, which employs 5,000 staff in 20 countries, has key growth projects in Brazil and Australia but its growing asset base has led to higher unit operating costs.
Its shares fell by more than 3% today after Mr Finlayson's departure and the company's updated guidance that production will be towards the lower end of expectations due to the ongoing issues in Egpyt.