In order to improve the robustness of Non-negative Matrix Factorization (NMF) algorithm for speech enhancement in different background noises, a speech enhancement algorithm based on Sparsity-regularized Robust NMF (SRNMF) was proposed, which takes into account the noise effect of data processing, and makes sparse constraints on the coefficient matrix to get better speech characteristics of the decomposed data. First, the prior dictionary of the amplitude spectrum of speech and noise were learned and the joint dictionary matrix of speech and noise were constructed. Then, the SRNMF algorithm was used to update the coefficient matrix of the amplitude spectrum with noise in the joint dictionary matrix. Finally, the original pure speech was reconstructed, and enhanced. The speech enhancement performance of the SRNMF algorithm in different environmental noise was analyzed through simulation experiments. Experimental results show that the proposed algorithm can effectively weaken the influence of noise changes on performance under non-stationary environments and low Signal-to-Noise Ratio (SNR) (<0 dB), it not only has about 1-1.5 magnitudes improvement in Source-to-Distortion Ratio (SDR) scores, but also is faster than other algorithms, which makes the NMF-based speech enhancement algorithm more practical.