A new hexapod robot mechanism was designed based on the leg structure and the gait movement characteristics of honeybee legs and the basic principles of bionics design, which can move forward, backward and turn in different locomotion gait and has high gait stability and environment adaptability. The kinematics model of the single leg of the robot was built by using the spatial decomposition method, and the unique solution of inverse kinematics was obtained by solving the model with elimination method. The movement trajectory of the foot end of hexapod robot was obtained by numerical solution, and the kinematics model was verified. Based on the characteristics of the movement gait of the honeybees, the movement gait of the hexapod robot in straight walking and turning was planned. The research provides a new idea and theoretical reference for the mechanism design and the gait planning of hexapod robots.