It’s always been a problem to improve the quality of enhanced speech in non-stationary noise and low SNR for speech enhancement research. In recent years, Convolutive Nonnegative Matrix Factorization algorithm has been well used for speech enhancement. Considering the sparsity of speech signals in the frequency domain, a speech enhancement method based on Sparse Convolutive Nonnegative Matrix Factorization(SCNMF) is proposed. Our method for speech enhancement consists of a training stage and a denoising stage. During the training stage, we model the prior information about the spectrum of speech and noise by SCNMF algorithm and the dictionary of speech and noise is constructed. During the denoising stage, the spectrum of noisy speech is analyzed by SCNMF algorithm, then, we use the dictionary of speech and noise to evaluate the coding matrix of speech, and reconstruct the enhanced speech. The impact of sparse factor on enhanced speech quality is analyzed through simulation experiments. Experimental results show that the proposed method outperforms traditional speech enhancement algorithms, such as MSS, NMF, CNMF, in non-stationary noise and low SNR.