Abstract: In the real world many data sources exist in the form of tensor, so the learning algorithm based on tensor space can describe the semantic information of data sources better. This paper presents a new tensor correlation analysis algorithm, with which we can directly analyze the tensor data. Because of the large reduction of the dimension of eigenvalue decomposition covariance matrix, the algorithm can effectively reduce the computing complexity and avoid the covariance matrix singular problem. The effectiveness of this method can be proved at YALE, ORL face database.