The problem of censored covariates arises frequently in family history studies as well as in longitudinal cohort studies. We develop inverse probability weighting (IPW) and augmented inverse probability weighting (AIPW) estimators for linear regression coefficients when a covariate is randomly censored. AIPW method enjoys the property of double robust by adding an augmented term to IPW method. The proposed AIPW estimator is consistent if either weight or augmented part is correctly specified, and obtains better efficiency than IPW estimator and complete-case regression estimator when both parts are correctly specified. For weight estimation, we propose kernel smoothing method, which outperforms Kaplan-Meier method in finite sample. Through extensive simulation studies, we show that proposed estimators have decent finite sample performance with better efficiency than complete-case regression estimator. In addition, we investigate the asymptotic properties of both estimators, and apply the proposed methods to a real data set.