To improve the identification capability of AP algorithm in time-varying sparse system, we propose a block parallel l 0 SWL- DCD-AP algorithm in this paper. In the proposed algorithm, we first introduce the l 0 norm constraint to promote its application for sparse system. Second, we use the shrinkage denoising method to improve its track ability. Third, we adopt the widely linear processing to take advantage of the non-circular properties of communication signals. Last, to reduce the high computational complexity and make it easy to implemented, we utilize the dichotomous coordinate descent (DCD) iterations and the parallel processing to deal with the tap-weight update in the proposed algorithm. To verify the convergence condition of the proposed algorithm, we also analyze its steady-state behavior. Several simulation are done and results show that the proposed algorithm can achieve a faster convergence speed and a lower steady-state misalignment than similar APA-type algorithm. When apply the proposed algorithm in the decision feedback equalizer (DFE), the bite error rate (BER) decreases obviously.