In order to express the spatial structure information of hyperspectral image more effectively and improve the classification accuracy after dimensionality reduction, we propose a hyperspectral feature extraction algorithm based on linear embedding and tensor manifold. Different from other manifold structure expression methods, the proposed algorithm uses the cooperative representation theory to solve the weight matrix for globally linear embedding, which is more beneficial to maintain the global information of high dimensional data and improve the accuracy of manifold structure expression. At the same time, the dimension reduction framework of tensor manifold based on multi-feature description is established, and the obtained explicit mapping has strong reliability and global adaptability. Experimental results show that compared with the principal component analysis, locally linear embedding, Laplacian Eigenmap, linearity preserving projection and other algorithms, the proposed algorithm has better classification performance.