Shape memory alloys (SMA) can generate displacement and force via phase change and have been widely used as actuators in robotics due to their light weight and ease of control. This paper proposes a SMA-driven crawling robot which activates antagonistic SMA springs alternately through a mechanical on-off logic switching system. By introducing a cam based bistable mechanism, elastic energy is stored and released to regulate the reciprocating motion of a slider in the robot. Meanwhile, the robot feet with anisotropic friction surface are employed to convert the reciprocating motion of the slider to unidirectional locomotion of the robot. The static model of the SMA and control logic of the robot are analyzed and validated through experiments.