Controlling the landing position of a spinning ball is difficult when using a table tennis robot. A complete physical model requires the factoring in of aerodynamic elements and object collisions, and inaccurate environmental coefficients would increase the landing position error. This study proposed a landing position control method based on a cascade neural network (CNN) that consists of forward and recurrent neural networks (RNNs). The forward NNs are used to estimate the velocity of the outgoing ball according to the velocity and acceleration of the incoming ball captured by cameras and the desired velocity of the outgoing ball. The RNN is employed to reverse-predict ball displacement based on the state of the incoming ball, desired landing point, and ball flight duration. The experiments verified that the method proposed in this study achieved control of differently spinning balls more effectively than the locally weighted regression (LWR)-based model did. The success rate of the CNN at two of six desired landing points was 25.9% and 32.9% higher, respectively, compared with use of the LWR-based model.