Compared with traditional wheeled and footed robots, spherical tensegrity robots have the advantages of high strength to mass ratio, good cushioning performance and good terrain adaptability, and have a broad application prospect in deep space exploration. Cable driven mode is often used for tensegrity robots, however, the excessive number of actuators in the walking process brings difficulties to the manufacturing and controlling. A new driving mode based on the post-buckling deformation of flexible rods is proposed, and the numerical simulation of the walking process of the spherical tensegrity robot is realized, and the efficiency of cable driven and rod-post-buckling driven mode is compared. The exact solution of post-buckling deformation of a single bar is obtained by elliptic integral method. Based on this, the rigid-flexible coupling dynamics simulation model of spherical tensegrity robot is established in ADAMS considering post-buckling deformation of the bar, contact and friction. The walking gait of the spherical tensegrity robot is determined by the joint simulation of ADAMS and Simulink software using the Greedy Search algorithm. The control system model is established in Simulink software to realize the walking control of the robot to any target points under the post-buckling driven mode of rods. Compared with the conventional cable driven, with post-buckling driven mode, the number of actuators required for continuous robot walking is reduced from 18 to 6, and the walking speed is increased by 43.78%. The results of the study provide theoretical guidance for the design and manufacture of the new tensegrity robots.