Summary: For median regression models that regress the median of the survival time or a transform thereof on the covariates, some semi-parametric estimators that include the intercept component are introduced when the survival time may be censored. These new median regression estimators do not require estimating the censoring distributions. They can be viewed as an extension of the sample median to the censored regression model. These estimators are based on some weighted empirical survival and hazard functions and are shown to be consistent and asymptotically normal. They performed very well in various numerical studies. The proposed procedures are illustrated in some real data examples.