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The objective function of classical nonnegative matrix factorization (NMF) is non-convexity, which affects the obtaining of optimal solutions. In this paper, we proposed a NMF algorithm, and this algorithm was based on the constraint of endmember spectral correlation minimization and endmember spectral difference max- imization. The size of endrnember spectral overall- correlation was measured by the correlation function, and correlation function was defined as the sum of the absolute values of every two correlation coefficient between the spectra. In the difference constraint of the endmember spectra, the mutation of matrix trace was slowed down by introducing the natural logarithm function. Combining the image decomposition error with the influences of end- member spectra, in the objective function the projection gradient was used to achieve NMF. The effectiveness of algorithm was verified by the simulated hyperspeetral images and real hyperspectral images.