In order to further reduce the solution space of non-negative matrix factorization (NMF), a NMF method based on preserving the intrinsic structure of invariant constraint and the piecewise smoothness constraint of the endmember spectrum of the hyperspectral image for hyperspectral unmixing is proposed. Firstly, a projection equation is used to describe the intrinsic structure of the hyperspectral image. Then the graph regularization is introduced to establish the relationship between hyperspectral image and abundance matrix, thereby preserving the intrinsic structure invariant of hyperspectral image. Secondly, the adaptive potential function in Markov random field model is used as a smoothing function to improve the smoothness of the endmembers spectrum. Finally, L_1/2 sparse constraint is used to promote the sparsity of the abundance matrix. To validate the performance of the proposed method, an experimental analysis is conducted on two real data sets. The results confirm the superiority of the method.