The work presents the wheeled walking frames that are supporting equipments, to be used by elderly people or handicapped in rehabilitation. Mostly, standard frames have weakness in walking on upward/downward slope. People often need power assistance on upward, and need secure walking support without falling on downward. The purpose of this paper is to develop a speed control assisting unit for wheeled walking frames by using the generalized internal model control (GIMC) with LQ control. By selecting appropriate parameter, the control method has various type of control scheme. Effectiveness of the assisting unit is confirmed by comparative experiments on upward and downward slopes. The result shows that the proposed method is effective on speed control for the assisting unit of wheeled walking frames.