A pivot device has a pivot axle fastened on a cover of a lap top computer, a seat fastened on a chassis of the computer, and a first ring and a second ring respectively mounted around the pivot axle. The second ring and an elastic device are respectively mounted on the seat, and the second ring has two cutouts. Two lugs are respectively defined on the first ring and correspond to the cutouts. A nub is formed on an outer circumference of the first ring so that the nub presses against the elastic device. Hence, the cutouts are mated with the lugs by pushing so that the cover can be raised or lowered to the chassis and can be controlled to prevent colliding with the chassis.