The actor attended the premiere in Los Angeles Monday night with his wife Luciana Barroso and three of their daughters.
Damon and Barroso are parents to four girls: Isabella, Gia, Stella and Alexia, who is Barroso's daughter from her previous marriage.
"Air," directed by Ben Affleck, tells the story of "the unbelievable game-changing partnership between a then-rookie Michael Jordan and Nike's fledgling basketball division which revolutionized the world of sports and contemporary culture with the Air Jordan brand."
In it, Damon plays Nike executive Sonny Vaccaro, while his good friend and collaborator Affleck plays Nike co-founder Phil Knight.
Affleck was also supported by his wife, global superstar Jennifer Lopez, at the premiere.
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The director seemed to have some fun on the carpet at the premiere.
In one hilarious moment captured by photographers, Affleck appeared to photobomb Jason Bateman while he was posing on the carpet with his wife Amanda Anka.
The cast of "Air" also posed for plenty of snaps during the star-studded premiere.
The film hits theaters April 5.