Penn: Hoping The Pledge will do well in Europe
The crime thriller, which premiéres on Thursday, stars Jack Nicholson and Penn's wife Robin Wright Penn.
The couple were expected to attend a press conference to talk about film, ahead of the evening's screening.
Penn gained something of a badboy reputation during the 80s when he was married to Madonna.
He served a prison sentence for attacking an actor on the set of the film Colors.
Although he appeared in a steady stream of films, it was his performance in films such as Dead Man Walking and Carlito's Way which gained him critical recognition.
He was Oscar-nominated for best supporting actor for Dead Man Walking in 1996 and best actor for Sweet and Lowdown in 2000.
The Pledge is Penn's third directorial outing, having written and directed The Indian Runner and The Crossing Guard, which also starred Nicholson and Wright Penn.
The Pledge sees Nicholson play a middle-aged police officer who vows to hunt down the killer of a young girl.
Penn describes it as a "no bad deed goes unpunished tale".
It opened earlier in the year in the US to mediocre box office sales.
But its entrance in the Cannes Film Festival in May saw it receive critical acclaim.
He is hoping his appearance in Edinburgh will boost audience figures in the UK when it goes on general release.
The festival has so far seen appearances from Billy Connolly and Tim Roth, who introduced a screening of Planet of the Apes.
Nicola Pierson, the film festival's head programmer, said: "We're all very excited and very pleased that Sean is coming to Edinburgh and bringing his family with him too.
"We've maybe had more glossy stars here before, but he is a huge star and also has huge integrity as an artist."