Bear Island by Alistair MacLean
(from the back of the book)
October is no time to be aboard ship in the Barents Sea, three hundred miles north of the Arctic Circle. But that's where the cast and crew of Olympus Productions find themselves. And even before they reach their destination, the ship's doctor has his hands full. Three men are violently murdered, and the company's unspoken fears are confirmed: a pathological killer awaits them on the loneliest, most desolate island in the world.
Does Bear Island guard a secret more valuable than five lives? Why is there no shooting script for the movie-and why has no one except the director been allowed to see the screenplay? Is the entire company marked for death? Does a mass murderer lurk in its midst, a pathological killer?