Bradley Cooper's more than just a pretty face ... he's got a pretty voice too.

Bradley literally put on a performance filming at The Greek Theater in L.A. for "A Star is Born."

It's interesting ... these kinda scenes are usually recorded in a studio and what's performed onstage is usually lip-synched. But Bradley here's doing the real thing ... at least from what we can hear.

He's a multi-tasker for sure, starring in the movie, making his directorial debut and also producing.