Aiming at efficient locomotion on the ground and safe stairs climbing for aged or physical disabled people, a wheel-track hybrid electric powered wheelchair (EPW) is designed, analyzed, and demonstrated extensively on various conditions. We first present the wheel-track hybrid design of the EPW with a focus on the mechanical structure and of onboard control system. We then discuss and analyze the wheel and the track mobile modes and their switching design of the EPW. The use of the track mobile mode is primarily for climbing up and down the stairs while the wheel mobile mode is for commonly ground surfaces. The mechanics analysis during these two mode switching and in the process of climbing up and down the stairs are also presented in the paper. The simulation and experimental results show that the new wheel-track hybrid EPW can effectively conduct the two locomotion modes including climbing up and down the stairs. The results also validate the motion mechanics calculation models and the dynamic mode switching between two mobile modes.