A hexapod robot with fewer actuators,good obstacle capability and good stability is designed.The whole structure of the hexapod robot with fewer actuators and the gait of walking are analyzed. On this basis,the equation of foot trajectory is established. The requirements of foot movement and obstacle crossing are obtained. The mathematical model of the foot trajectory of the hexapod robot with fewer actuators is established.The trajectory optimization model of foot trajectory for the stability of hexapod robot movement is established considering five types of constraints-the rod length,transmission performance,geometric structure,obstacle and boundary conditions. By using MATLAB optimization toolbox constraint fmincon function,the parameters effecting the foot trajectory of the hexapod robot with fewer actuators are optimized. The dimensions of leg mechanism of the hexapod robot that meet the kinematic characteristics requirements are obtained. The rationality of the leg mechanism is proved by the analysis of the optimized foot trajectory. All of these provide the foundation for the following research and development of the hexapod robot.