To improve the obstacle avoidance ability and path planning efficiency of mobile legged robots, a convex optimization and A-star algorithm combined path planning and obstacle avoidance algorithm is proposed. Firstly, a method of iterative regional inflation by semi-definite programming(IRI-SDP) is presented to quickly compute out a large convex polygon of obstacle-free and its largest inscribed ellipse in the given ground environment through alternating two convex optimizations. The obstacle-free region is utilized for obstacle avoidance and task motion planning locally. Then, combining with the classical A-star algorithm via establishing the local and world coordinate system of mobile robots, the transfer model of the mass center of mobile robots, the impact model and the heuristics cost function, the optimal minimum-cost path in the global environment can be found. Finally, simulation results validate the effectiveness of proposed method.