Abstract: The l0 and l1 norm constrained least mean square (LMS) algorithm can effectively improve the performance of the sparse channel estimation, but the convergence performance of such algorithms will considerably vary when the channel exhibits different sparisity. A novel p-norm like constraint LMS algorithm to accommodate the various sparisity of the channels through the introducing of the variable p-value was presented. Furthermore, the gradient guided optimization of the p-value was derived. Numerical simulation results are given to demonstrate the superiority of the new algorithm.