Damon stars as a rogue Army officer searching for weapons of mass destruction in Iraq a few weeks after the 2003 U.S. invasion.
For Damon, the movie is exciting because of the way Greengrass works.
"You never know what's going to happen, even as an actor, in his movies," said Damon. "He's got a very loose way of working, a liberating way of working, you're kind of flying by the seat of your pants a lot."
Greengrass says that in the end, big movies should be the cinematic equivalent of an amusement park ride.
"You've got to go up and down, faster and slower," said Greengrass. "If you don't feel the ride you're not going get to the end and feel satisfied, you're not going to feel it's a worthwhile evening in the theater."
Damon's character has a take-charge attitude in dealing with the war. And the actor got to spend time working many real soldiers. In real life, he's a bit more laid back.
"What I noticed about all the guys who'd just come back from Iraq and Afghanistan, they're just very 'on the front foot,' so to speak. Go-getters, and I think I do tend to sit back and relax," said Damon.
"Green Zone" is Rated "R" and is in theaters now.