Delivery is scheduled to begin in 2016 and includes 30 orders for the A320neo, the latest version of Airbus's popular airplane, The New York Times reported.
The A320neo has a more fuel-efficient engine that is expected to reduce fuel consumption by 15 percent, Airbus said.
Last week Airbus, based in Toulouse, France, announced a record order from IndiGo, a low-cost carrier in India that said it would buy 180 A320s, including 150 with the new engine.
The list price of the Burlingame, Calif.-based Virgin America order with Airbus is $5.1 billion, but Airbus does not reveal the actual sale price for competitive reasons, the Times said.
Industry analysts and rival Boeing have questioned whether Airbus really could meet the targeted fuel savings with its new plane, citing the heavier wings required to accommodate larger engines, the Times said.
John Leahy, Airbus's top sales representative, dismissed the criticism.
"I am really frustrated that some people in the industry are saying this is not such a good business case," Leahy said. "There has never been an aircraft with 15 percent fuel cuts that was not a huge success. We are a little frustrated that our competitor is wringing its hands, wondering whether the business case is worthwhile."