In this paper, we develop a robotic table tennis system in the case of the back spin with the same measurement method and the ball models of the aerodynamics and the rebounds as in the study of Nakashima et al. (2011). First, the aerodynamics model is improved for precise prediction of the ball trajectory with data of the flying back-spin ball. Second, a method to determine the racket motion is shown where approximated inverse problems of the models are solved with optimizations. Third, a motion planning of the robot to achieve the racket motion is proposed with the velocity limitation of the robot joints. Experimental results are shown to verify the effectiveness of the proposed method.