A magnetic field in the range from 0.5 to 2.0 teslas is applied for the annealing process of GMR and TMR thin film. The conventional water-cooled resistive magnet for the process at the level of 1.5 teslas weighs more than 8 tons, and requires electric power of 100 kW and cooling water of 140 liters per minute. Thus, a light-weigh magnet having low electricity and water consumption was required. We have developed a cryocooled superconducting magnet having half the weight and one-tenth the power and water consumption of the conventional one.