The existing Nonnegative Matrix Factorization （NMF） algorithms are often designed based on Euclidean distance， which makes the algorithms sensitive to noise. In order to enhance the robustness of these algorithms， a Manifold Regularized Nonnegative Matrix Factorization based on Clean Data （MRNMF/CD） algorithm was proposed. In MRNMF/CD algorithm， the low-rank constraints， manifold regularization and NMF technologies were seamlessly integrated， which makes the algorithm perform relatively excellent. Firstly， by adding the low-rank constraints， MRNMF/CD can recover clean data from noisy data and obtain the global structure of the data. Secondly， in order to use the local geometric structure information of the data， manifold regularization was incorporated into the objective function by MRNMF/CD. In addition， an iterative algorithm for solving MRNMF/CD was proposed， and the convergence of this solution algorithm was analyzed theoretically. Experimental results on ORL， Yale and COIL20 datasets show that MRNMF/CD algorithm has better accuracy than the existing algorithms including k-means， Principal Component Analysis （PCA）， NMF and Graph Regularized Nonnegative Matrix Factorization （GNMF）.