To realize the omnidirectional motion, the transition motion of hexapod robot from flat to slope is studied, and a new type of stability criterion is proposed. Firstly, the landing point problem of the hexapod robot in the process of transition is studied, the relationship between the introduced angle in ankle of the supporting leg and the body pitch is acquired, and the transition gait based on central pattern generator bottom feedback is planned. Secondly, the slope motion is analyzed, the relationship between the angle variable of the supporting knee joint and the pitch angle of hexapod is obtained, and the slope gait is planned based on central pattern generator middle level feedback. According to vector product, the solution of working out the stability margin of hexapod robot’s motion is designed. Lastly, MATLAB/ADAMAS co-simulation platform and physical hardware are constructed, the simulation and experiment of transition motion of hexapod robot from flat to 12° slope and motion of climbing 16° slope are done. According to the analysis of the results, in the transition motion from flat to 12° slope, based on the transition gait, hexapod robot can keep three foots touch the ground, and the foot force is uniform. According to the means designed to work out a stability margin based on vector product, the stability margin constant is greater than zero. In the motion of climbing 16° slope, based on the slope gait, hexapod robot completes the motion of climbing 16° slope. Based on transition gait, hexapod robot implements the transition movement from flat to slope stably. Based on slope gait, hexapod robot improves the ability of slope motion.