Abstract: A single-channel speech enhancement approach is presented, where a novel convolution non-negative matrix factorization algorithm with L_1/2 sparse constraint is proposed, aiming at characterizing the inter-correlation of the speech signal and using less basis to present the speech signal. The noise basis is obtained firstly by training the noise, the speech basis is learnt from noisy speech by using the proposed approach combined with pre-trained noise basis. Then, the enhanced speech is reconstructed by the speech basis and its corresponding coefficients. Experimental results in different noise environments show that the proposed approach outperforms the convolution non-negative matrix factorization algorithm with L₁ sparse constraint and conventional statistical speech enhancement algorithms.