In this paper, we extend the random weighting method to linear errors-in-variables models and propose random weighting M-estimators (RWME) for parameters. Its large sample properties are studied and the consistency and asymptotic normality are proved under mild conditions. In addition, the results facilitate the construction of confidence regions and hypothesis testing for the unknown parameters. Extensive simulations are reported, showing that the proposed method works well in practical settings. The proposed methods are also applied to a data set from an AIDS clinical trial group study.