In this research, we present a novel soft robot actuated by shape memory alloy (SMA) springs, which can achieve several different locomotion. The robot can perform inching, crawling, and undulating motions by independently controlling four SMA springs. The SMA springs are arranged in an antagonistic configuration to provide clockwise and counterclockwise motions. Front and rear legs with claws are designed to adjust to friction forces between the robot and the ground, which is essential for the locomotion of the robot. Including one undulatory, three inching, and two crawling locomotions, six locomotion strategies are then implemented in the bang-bang control structure. The applied bang-bang controllers switch control inputs to the robot based on feedback from the orientation angle of the robot body or the SMA temperature. All loco- motion strategies were experimentally validated. The performance of the six locomotion strategies were investigated and compared. Our results show that the fast inching gait can provide a higher velocity and longer tread per gait cycle when compared to the other locomotion strategies.