In the system design of table tennis robot, the important influencing factors of automatic detection of technical and tactical indicators for table tennis are table tennis rotation state, trajectory, and rebound force. But the general prediction algorithm cannot process the time series data and give the corresponding rotation state. Therefore, this paper studies the automatic detection method of technical and tactical indicators for table tennis based on the trajectory prediction using the compensation fuzzy neural network. In this paper, the compensation fuzzy neural network algorithm which combines the compensation fuzzy algorithm and recurrent neural network is selected to construct the automatic detection of technical and tactical indicators for table tennis. The experimental results show that the convergence time of the compensation fuzzy neural network is shorter, the training time is shortened, and the prediction accuracy is improved. At the same time, in terms of performance testing, the model can accurately distinguish the influence of table tennis rotation state and rebound on table tennis motion estimation, so as to improve the accuracy of motion trajectory prediction. In addition, the accuracy of trajectory prediction will be improved with the increase of input data. When the number of data reaches 30, the trajectory prediction error is within the actual acceptable error range.