Non-negative　matrix　factorization　(NMF)　is　a　recently　developed　technique　for　finding　parts-based,　linear　representations　of　non-negative　data.　In　this　paper,　we　present　a　fast　algorithm　to　solve　local　learning　regularized　nonnegative　matrix　factorization.　We　consider　not　only　the　local　learning,　but　also　its　convergence　speed.　Experiments　on　many　benchmark　data　sets　demonstrate　that　the　proposed　method　outperforms　the　local　learning　regularized　NMF　in　convergence　speed.