The problem of censored covariates arises frequently in family history studies, in which an outcome of interest is regressed on an age of onset, as well as in longitudinal cohort studies, in which biomarkers may be measured post-baseline. Use of censored covariates without any adjustment is well known to lead to bias in estimates of the coefficients of interest and inflated type I error. Multiple imputation has gained its popularity in dealing with censored or missing covariates. However, commonly used multiple imputation methods are sensitive to the model specification. It may lead to large bias in regression coefficient estimation if the imputation and the substantive models are incompatible. We proposed a fully conditional specification method for multiple imputation without parametric assumption on the distribution of randomly censored covariates. The proposed method can avoid model misspecification issue in multiple imputation, ensuring the compatibility of substantive and imputation models. A rejection sampling strategy is applied to approximate the imputation model in the proposed method. Through simulation studies, we compare the proposed method with other existing method.