In high-dimensional settings, penalized least squares approach can lose its efficiency in both estimation and variable selection due to the existence of heteroskedasticity. In this manuscript, we propose a novel approach, penalized adaptive weighted least squares (PAWLS), for simultaneous robust estimation and variable selection. The proposed PAWLS is justified from both Bayesian understanding and robust variable selection points of view. We also establish oracle inequalities for both regression coefficients and heterogeneous parameters. The performance of the proposed estimator is evaluated in both simulation studies and real examples.