A military police officer reportedly shot his wife to death after brutally beating her during a heated confrontation in Brazil ... and it was all caught on video.

Thiago Cezar de Lima was off-duty Sunday when he started arguing with his wife, Erika, for some reason inside a parked car in Sao Paolo.

Check out the surveillance footage ... Erika jumps out of the driver's seat and circles around the car, ripping open a passenger side door and trying to yank Thiago out of the backseat.

The two get into a violent struggle as Thiago pops out of the vehicle with a pistol gripped in his hand. Thiago repeatedly punches Erika in the head before aiming the gun at her.

Thiago reportedly loaded Erika into the car and drove her to a local hospital, where she was pronounced dead.