Least mean square (LMS)-type adaptive sparse algorithms have been attracting much attention on sparse multipath channel estimation (SMPC) due to their two advantages: low computational complexity and reliability. By introducing ℓ1 -norm sparse constraint function into LMS algorithm, both zero-attracting least mean square (ZA-LMS) and reweighted zero-attracting least mean square (RZA-LMS) have been proposed for SMPC. It is well known that the performance of the SMPC is decided by regularization parameter which balances channel estimation error and sparse penalty strength. However, optimal regularization parameter selection has not yet considered in the two proposed algorithms. Based on the compressive sensing theory, in this paper, we explain the mathematical relationship between Lasso and LMS-type adaptive sparse algorithms. Later, an approximate optimal regulation parameter selection method is proposed for ZA-LMS and RZA-LMS, respectively. Monte Carlo based computer simulations are presented to show the effectiveness of our propose method.