This paper considers a novel model predictive control method for a high-speed magnetic actuator. The actuator consists of two opposing electromagnets and an armature is suspended between them. The armature reciprocates between the two magnets. The armature is suspended by the springs with a large spring rate, enabling it to move at high speed. A difficulty is that push-pull control force for the armature is not available from the electromagnets. Additionally, magnetic force is effective only when the armature is very close to the pulling magnet. To overcome those difficulties, we propose a controller using model predictive control method with a fixed compensator. Based on optimality, the model predictive controller generates a target trajectory with searching for the terminal time, and a fixed compensator is attached in order to improve robustness drastically.