This paper presents a novel dictionary learning (DL) method to improve the performance of sparsity based single-channel speech separation (SCSS). The conventional approaches regard the sub-dictionaries as independent units and learn sub-dictionaries separately in the short-time Fourier transform (STFT) domain using their corresponding training sets respectively. However, we take the relationship between the sub-dictionaries into account and optimize the sub-dictionaries jointly in the time domain. By satisfying a designed discrimination constraint, a structured dictionary, whose atoms have better correspondences to the speaker labels, is learned so that the sources can be recovered by the corresponding reconstruction after sparse coding. An algorithm, which consists of sparse coding stage and dictionary updating stage, is proposed to deal with this DL optimization problem. Two strategies, i.e., direct learning and adaptive learning, are presented to select the training sets which are used to learn the discriminative dictionary. Experimental results show that the proposed SCSS algorithms have superior performance compared with other tested approaches.