Abstract: Due to limitations in material properties and driving principles of soft robots, it is difficult to improve their motion performance and load-carrying capacity. To address this issue, a pneumatic soft quadruped robot based on a bistable actuator is proposed. Firstly, a bistable soft actuator composed of rigid links, soft actuators and springs is designed. The actuator can utilize springs for energy storage and quickly jump between two stable states under the drive of compressed air. The theoretical energy model of the actuator is derived, and the prototype is tested. The test results show that the jump motion time of the bistable soft actuator is 60\sim 100 ms, and the end output force is 2\sim 4 times that of the soft actuator under the same driving conditions. Then, a quadruped robot based on this actuator is designed, and the control scheme and motion gait of the robot are analyzed. Finally, a pneumatic control circuit is constructed to test the performance of the quadruped robot prototype. The research results demonstrate that the prototype can creep 125 mm or turn 15^\circ in one motion cycle, with an average creeping speed of 158.62 mm/s (1.11 times body length/s) and a peak instantaneous speed of 396.62 mm/s (2.83 times body length/s). In addition, the robot can carry a load of 400 g, equivalent to 1.08 times its own mass, demonstrating good motion performance and load-carrying capacity.