Abstract: We propose a composite robust reactive control strategy with disturbance rejection to solve the balance recovery problem of the quadruped robot under lateral disturbance. The proposed strategy has two parts: An adaptive lateral motion planning strategy for the swinging phase and joint robust control for the supporting phase. The swing-phase adaptive lateral motion planning strategy gives the starting conditions of the lateral motion based on the joint output torque, and performs active gait planning based on the force balance conditions of the foot of the quadruped robot to ensure the stability of the robot's posture under lateral disturbance. The supporting-phase joint control compensates for the lateral disturbance of the supporting leg joint via a robust sliding mode controller, which has a disturbance observer based on a complete dynamic model of the quadruped robot that includes a disturbance term to ensure the stability of the quadruped robot under lateral disturbance. The effectiveness of the proposed control strategy is verified by a co-simulation of Matlab and ADAMS.