Quantile regression techniques have been widely applied in empirical economics. In this paper we consider the estimation of a generalized quantile regression model when data are subject to fixed or random censoring. Through a discretization technique we transform the censored regression model into a sequence of binary choice models and further propose an integrated smoothed maximum score estimator by combining individual binary choice models corresponding to different cutoff points, following the insight of Horowitz (1992) and Manski (1985) for the estimation of the binary choice model under quantile regression. Unlike the estimators of Horowitz (1992) and Manski (1985), our estimators converge at the usual parametric rate through an integration process. In the case of fixed censoring, our approach overcomes a major drawback of existing approaches. Our approach for the fixed censored case can be extended readily to the case with random censoring for which other existing approaches are no longer applicable. Both of our estimators are consistent and asymptotically normal. A simulation study demonstrates that our estimators perform well in finite samples.