Heat an iron and place it over the peeling laminate. Smooth from the inside of the desk and work toward the edge. If the adhesive is still intact this will be the only step you need to repair your laminate. If the laminate does not stick after ironing, continue to the next step.
Peel back the corners of the laminate. Be careful not to tear them. Use a knife to scrape off the old adhesive from the desk top.
Apply contact adhesive to the desk and the underside of the laminate. Keep the pieces separated until the adhesive is no longer tacky. Then press the two pieces together, smoothing the laminate down from the inside working toward the edge. Smooth out any air bubbles. Place a heavy object on the area until the glue sets.