The purpose of this paper is the rotor design of a single-phase LSPM(Line-start permanent magnet) motor. A single-phase LSPM motor has a permanent magnet in the rotor that is same as induction motor. For that reason, magnet is operated by breaking torque in starting region and alignment torque in driving region. Therefore, we need the design process considering the trade-off relationship. In this paper, we propose the design process of a single-phase LSPM motor for a high starting torque and efficiency with FEM. And we use Taguchi Method for considering tolerance in manufacture. Finally, we compared the LSPM motor that is designed in this paper and conventional induction motor.