In this work, a multiple speech source separation method using inter-channel correlation and relaxed sparsity is proposed. A B-format microphone with four spatially located channels is adopted due to the size of the microphone array to preserve the spatial parameter integrity of the original signal. Specifically, we firstly measure the proportion of overlapped components among multiple sources and find that there exist many overlapped time-frequency (TF) components with increasing source number. Then, considering the relaxed sparsity of speech sources, we propose a dynamic threshold-based separation approach of sparse components where the threshold is determined by the inter-channel correlation among the recording signals. After conducting a statistical analysis of the number of active sources at each TF instant, a form of relaxed sparsity called the half-K assumption is proposed so that the active source number in a certain TF bin does not exceed half the total number of simultaneously occurring sources. By applying the half-K assumption, the non-sparse components are recovered by regarding the extracted sparse components as a guide, combined with vector decomposition and matrix factorization. Eventually, the final TF coefficients of each source are recovered by the synthesis of sparse and non-sparse components. The proposed method has been evaluated using up to six simultaneous speech sources under both anechoic and reverberant conditions. Both objective and subjective evaluations validated that the perceptual quality of the separated speech by the proposed approach outperforms existing blind source separation (BSS) approaches. Besides, it is robust to different speeches whilst confirming all the separated speeches with similar perceptual quality.