To achieve the trotting locomotion of the quadruped robot with an active spine on the rough deformable terrain, a central pattern generator (CPG) based control method was proposed by the kinematics analysis, including six modules: gait planning, ground inclination estimator, posture control, stumbling reflex, step-missing reflex, and lateral stepping reflex. The gait planning module was used to generate the joint signals of legs and spine. The ground inclination estimator was used to calculate the ground inclination and adjust the planned foot trajectory according to the ground inclination. The posture control module made the body parallel to the ground and control the heading angle of the robot. The stumbling reflex made the legs cross barriers and then return to the planned motion trajectory quickly when they came in contact with barriers in the swing phase. The step-missing reflex made the legs contact with the ground and then return to the planned motion trajectory quickly when they missed their steps in the stance phase. The lateral stepping reflex eliminated the effects on the external force, preventing the robot from capsizing sideways. By making the robot move in different terrains, the control parameters of each module could be adjusted and determined step by step. The simulation results show that the quadruped robot with an active spine can successfully cross the structured terrain,including external interference, steps, slopes, and stairs, the rough terrain simulated by rectangular triangular prisms randomly arranged at different angles, and the rough deformable terrain simulated by rectangular triangular prisms randomly arranged at different angles and spheres with the proposed method. © 2020, Editorial Department of Journal of Southeast University. All right reserved.