Abstract: Speech enhancement algorithms for dual small microphone arrays usually rely on the voice activity detection(VAD), and they may fail in some cases when target speech signal is included in the first frame. A multi-task sparse representation based speech enhancement algorithm was proposed. First, dictionaries for signal and noise were respectively formed via dictionary learning. Then the noise in signals obtain from two microphones was reduced by regularized sparse representation on the over-complete dictionary, while the target speech signals were mostly preserved, hence the speech signals were enhanced. Experimental results from synthetic and real-world data show that the proposed speech enhancement algorithm without VAD works well in all cases no matter speech signal is included in the first frame or not.