Recently, considerable attention has been devoted to quantile regression under random censoring in both statistical and econometrical literature yet little has been done on the important problem of model checking.In this talk, we will introduce a nonparametric test for checking the lack-of-fit of the quantile function of the survival time given the covariates when the survival time is subjected to random right censor ing.The test statistic is a kernel-based smoothing estimator of a moment condition.The test has an asymptotic normal distribution under the null hypothesis.Its power property is investigated through its behavior under local alternative sequence.We will also introduce a locally weighted censored quantile regression approach for es timation.The new approach adopts the redistribution-of-mass idea and employs a local reweighting scheme.