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Control of a space robot without actuators on the main body is an underactuated control problem. Various stabilization methods, such as the time-varying feedback control method, discontinuous feedback control method, center manifold-based method, zero-dynamics method and sliding-mode control method have been proposed. However, past studies have not considered underactuated space robots equipped with a flexible appendage, such as solar panels. If the manipulators are simply controlled to achieve the target state for the robot using the past controllers without taking a flexible appendage into consideration, residual vibration remains even after the link motion has finished. In order to suppress the residual vibration on the flexible appendage, we apply the input-shaping technique to the link motion of an underactuated planar space robot. Numerical and experimental studies are carried out to validate the proposed method for a planar duallink space robot with a flexible appendage. The results show that the proposed method is capable of not only controlling the link angles and the main body attitude to the goal angles, but also suppressing the residual vibration on the flexible appendage.