Greg Hardy MMA Training with 'Bigfoot' Silva (PHOTO + VIDEO)

Greg Hardy is taking his MMA training up a notch -- working on his fighting style with Antonio "Bigfoot" Silva ... and we've finally got video of the ex-NFL star in action.

Hardy has been working out with American Top Team in Florida -- hoping to take a pro MMA fight sometime in the future.

We're told he's been taking his training VERY seriously ... and our sources say he's winning over people at the gym. The fighters and the coaches really like him.

Still no word on what his pro fighting timetable is ... but hopefully we'll see him in action before the end of the year.