In this paper, we develop the control system of a stair-climbing inverted pendulum robot using a planetary wheel mechanism. The purpose of the control system is to ensure that the robot adjusts its orientation towards a given step before climbing the step and keep its main body stable before and after performing the climbing maneuver. The proposed system operates as follows. We utilize a state feedback control with a reference speed input and additional torque in order to guarantee the stability while moving and performing climbing maneuver. We use a proportional-derivative controller to control the orientation of the robot towards the stairs before climbing and to maintain the same orientation after the ascent or descent. Experimental results confirmed that the robot successfully ascended and descended the stairs by using the proposed method, even though the angles of each step's riser surface varied.