Nonnegative Matrix Factorization (NMF) is an effective matrix decomposition technique which has been widely used in many fields including image processing,text mining,pattern analysis and so on.Based on the projection of function gradient,we propose a novel projected gradient method for solving nonnegative linear least squares problem,and analyze its convergence properties.Applying the developed projected gradient method to the NMF problem,we present a new alternating projected gradient method for computing NMF.Numerical results show that the proposed method is superior to both the multiplicative update algorithm and the projected gradient method for the NMF.