A robotic wheelchair with inverse pendulum control has been proposed in this paper. By using the robotic wheelchair, a wheelchair-bound person can climb over a step up to about 7 cm without a helper's assistance. The robotic wheelchair moves on flat ground using four wheels. It raises its front wheels in front of a step, and maintains the inverse pendulum control. A user riding can go forwards and backwards using his/her body inclination maintaining the inverse pendulum control. The inverse pendulum control is stopped when the front wheels proceed over a step. After the front wheels land on the step, the robotic wheelchair can climb over the step, assisted by DC motor force. In order to raise the front wheels using small DC motors, the robotic wheelchair can move its rear wheel drive shafts. This paper presents the experiments on step climbing, the modelling of the control system, and the simulations on the inverse pendulum control. The step climbing function of the proposed robotic wheelchair has been successfully tested.