Bio-inspired jumping robots should achieve stable jumping in field environment. Robots easily lose stability because of the complex terrain and large speed change. Lateral jumping of the robot with four-bar jumping legs under rugged terrain was used as the research object, and a method to achieve good dynamic stability by adjusting the leg attitudes of the robot was proposed. The stability criteria were proposed hierarchically on the basis of the analysis of the jumping mechanism of creatures. Then, the dynamic model of the robot jumping on the slope was established, and the effect of different parameters on dynamic stability was analyzed to carry out the primary selection of parameters. Then, the method of maintaining dynamic stability was proposed. On the basis of ensuring large motion distances and stable driving torques, leg attitudes were considered the optimization parameters. Thus, the robot does not overturn or turn over uncontrollably in the take-off, buffering, and flight phases. Analysis results of robot jumping in plane and 3D space under different terrains prove the feasibility of this method. In particular, the dynamic stability of the robot is better if the take-off direction is considered an optimization parameter. The simulation results also proved the accuracy of the analysis results. The research results provide a theoretical basis to realize stable continuous jumping of bio-inspired biped robots.