Because of the skewness of the distribution of medical costs, we consider modeling the median as well as other quantiles when establishing regression relationships to covariates. In many applications, the medical cost data are also right censored. In this article, we propose semiparametric procedures for estimating the parameters in median regression models based on weighted estimating equations when censoring is present. Numerical studies are conducted to show that our estimators perform well with small samples and the resulting inference is reliable in circumstances of practical importance. The methods are applied to a dataset for medical costs of patients with colorectal cancer.