In this study, adaptive one-step generalized M-estimators for the regression parameters of the linear regression model are derived. The proposed estimators are developed assuming the exponential power family and the t-distribution family. A class of one-step M-estimators with likelihood score function is obtained then the estimators are adapted to the distribution. A Monte Carlo simulation study is conducted to investigate the performance of the suggested estimators. The results show that the proposed adaptive robust estimators are highly efficient than least squares estimators as well as robust counterparts. The results show also that the suggested method for estimating the shape parameter through its relation with the kurtosis coefficient gives efficient estimators.