A lower extremity exoskeleton robot is designed in order to help the lower limbs to restore the walking function of paralyzed people. According to the human body motion mechanism, the degree of freedom (DOF) of each joint was designed. The active joint and passive joint types were determined and the appropriate driving method was selected. The structural design of the main part was introduced in detail. The working mechanism and working mode of the robot were discussed. The linkage model of the lower extremity exoskeleton robot was established, and the joint motion trajectory was planned and the rotation motion curves of each joint were further solved. The gait curve of the plan was simulated and analyzed by the simulation software ADAMS. The simulation results show that the motion curves of each joint are smooth and without obvious impact. Comparing with the theoretical calculation value in one cycle, the error value of the angle simulation value of each joint is less than ±1.5°, within the reasonable error range. The curve-of-growth (COG) theory is used to verify the dynamic stability of gait trajectories and the rationality of the planned gait curve is also proved.