Conventional non-negative matrix factorization algorithms suffer from slow convergence in high-dimensional data dimensionality reduction. In this paper, a novel algorithm is proposed to accelerate the convergence speed. Firstly, non-negative matrix factorization is divided into two convex problems. Secondly, we construct estimate sequences to optimize each sub-problem. Thirdly, we alternately solve each sub-problem until convergence. Each sub-problem is optimized with Lipshcitz continuous, and its convergence rate is demonstrated at O(1/k2). The clustering experiment shows the effectiveness and fast convergence of the proposed algorithm.