In this paper, an active set recognition technique is suggested, and then a modified nonmonotonic line search rule is presented to enhance the efficiency of the nonmonotonic line search rule, in which we introduce a new parameter formula to attempt to control the nonmonotonic degree of the line search, and thus improve the chance of discovering the global minimum. By using a modified linear search and an active set recognition technique, a global convergence gradient solution for nonnegative matrix factorization (NMF) based on an alternating nonnegative least squares framework is proposed. We used a Barzilai-Borwein step size and greater step-size tactics to speed up the convergence. Finally, a large number of numerical experiments were carried out on synthetic and image datasets, and the results showed that our presented method was effective in calculating the speed and solution quality.