A human action recognition method based on a probabilistic topic model is proposed. Firstly, the method extracts space-time interest points to describe human motion. Then the slow feature analysis algorithm was proposed to calculate the invariant optimal solution of the gradient information of space time points. Lastly human actions were recognized with the probabilistic latent semantic analysis(pLSA). The invariant optimal solution of the gradient information can express the inherent characteristics of STIP, and it can also reflect the space and time information of STIP discriminatively. For solving the problem of latent topics that are not guaranteed in pLSA, the topics obtained in supervised fashion correspond to action labels one by one. Action recognition results were presented on KTH human motion data set and Weizmann human action data set. Our results show that the action recognition rates of the tow dataset are respectively more than 91.50% and 97%. 