Aiming at the problem that the operation scale of Robust Non-negative Matrix Factorization (RNMF) increases with the number of training samples, an incremental robust non-negative matrix factorization algorithm with sparseness constraints was proposed. Firstly, robust non-negative matrix factorization was performed on initial data. Then, the factorized result participated in the subsequent iterative operation. Finally, with sparseness constraints, the coefficient matrix was combined with incremental learning, which made the objective function value fall faster in the iterative solution. The cost of computation was reduced and the sparseness of data after factorization was improved. In the numerical experiments, the proposed algorithm was compared with RNMF algorithm and RNMF with Sparseness Constraints (RNMFSC) algorithm. The experimental results on ORL and YALE face databases show that the proposed algorithm is superior to the other two algorithms in terms of operation time and sparseness of factorized data, and has better clustering effect, especially in YALE face database, when the clustering number is 3, the clustering accuracy of the proposed algorithm reaches 91.67%.