In this study, we propose a fuzzy control design for a table tennis robot to accurately strike ping-pong balls, regardless of whether they are topspinning or backspinning. The classification of topspin and backspin is determined through a comparison of ball trajectories measured by binocular vision with that of an ideal flying model derived from aerodynamics. By inputting trajectory features into the corresponding model, the striking signal, including contact position and hitting time, can be predicted. A fuzzy inference system is then utilized to derive the face angle of the racket at the hitting moment, which ultimately controls the robot to strike topspinning or backspinning balls. With an average error of approximately 3 cm for contact position prediction and less than 13.5 ms for hitting time prediction, our proposed fuzzy control design has demonstrated its effectiveness in striking spinning balls.