Actor Bruce Willis poked fun at Dick Cheney's recent shooting accident by appearing on The Late Show With David Letterman made-up like the US vice president's hunting victim Harry Whittington.

The actor had tiny wounds on the left side of his face, resembling a spray of buckshot holes and when he smiled he revealed one tiny hole in his front tooth where he was allegedly hit by the ammunition.

Willis joked, "I got shot." He then lifted his hat to reveal his semi-bald head covered in band-aids, adding, "Shot all my hair off."

The Die Hard actor went on to explain, "I was playing cards with some politician guys, sitting around drinking all night.

"After a bottle and half of Jack Daniels, somebody came up with the idea, 'Let's go hunting.' It seemed like such a good idea at the time...

"I'm thinking we're going to go out and hunt rhino or moose, (but we hunt) quail.

"But it's all really a blur to me."