Abstract: Inspired by the quadruped locomotion, an adaptive control algorithm was proposed to adjust the trot gait of a quadruped robot on a slope automatically. The transverse and longitudinal displacement compensation adjusted by policy gradient via the signed derivative (PGSD) was introduced in the trajectory of the center of mass (COM) of the robot. The displacement compensation was arranged to reduce the robot's turning moment and time difference between the two diagonal legs landing, and to improve the stability of robot locomotion. The simulation of the robot locomotion was performed with a simulation software Webots. The simulation results show that the adaptive control algorithm proposed in this paper can effectively improve the locomotion stability of the quadruped robot on a slope.