Laver, who won all four major tournaments in a calendar year on two occasions during his playing days, believes that Murray will win a lot more titles before he retires from the game.
"A few years ago when I watched Murray losing in Grand Slam finals, I never doubted he had the ability to beat the world's best players – Roger Federer Rafael Nadal, and Novak Djokovic – in big matches, but my one reservation about Murray was his lack of self belief and his failure to play enough 'kill' shots when he was on top," Laver told The Scotsman.
"I now believe Murray has proved he does have both the self-belief and the aggression needed to beat anybody. He's also shown that he knows how to handle the pressure on crucial points because he's a smarter player than before when he seemed to find ways to lose finals he should have won as his form went up and down like a yo-yo.
"The difference with Murray is that now he's got two majors to his name, including the big one, Wimbledon, so that should give him the confidence to go on and win more grand-slam tournaments. I would be very surprised if he didn't."
Murray is currently ranked as number two in the world.