With sharply increasing of elderly and disabled people at present, the work which focuses on making life easier for those people have been paid more attention. So a new stair-climbing wheelchair was designed in this paper which can work in three modes: stair-climbing mode, powered wheelchair mode and manual mode. It helps physically disabled and elderly people to move more flexibly and comfortably. The walking mechanism was first designed in this paper, as well as the theoretical design and calculation which was used to decide the structure and dimension; then transmission system design was followed. An optimization design for the planetary wheels mechanism is carried out based on the model which was modelled in software Autodesk Inventor. A seat backrest adjustment system was designed to adjust the centre of gravity before climbing up and down stairs. At the same time, a locking system was installed to make the wheelchair working more safety. Computer simulations were performed to evaluate this design. Stress analysis for different materials of the frame was carried out in inventor, in order to realize optimal selection for the material. Finally animation was made to show how the wheelchair works in different situations.