This paper studies an M-estimation-based method for linear estimation with weighted L1 regularization and its recursive implementation. Motivated by the sensitivity of conventional least-squares-based L1-regularized linear estimation (Lasso) in impulsive noise environment, an M-estimator-based Lasso (M-Lasso) method is introduced to restrain the outliers and an iterative re-weighted least-squares (IRLS) algorithm is proposed to solve this M-estimation problem. Moreover, instead of using the matrix inversion formula, QR decomposition (QRD) is employed in the M-Lasso for recursive implementation with a lower arithmetic complexity. Simulation results show that the M-estimation-based Lasso performs considerably better than the traditional LS-based Lasso in suppressing the impulsive noise, and its recursive QRD algorithm has a good performance in online processing.