In　this　article,　we　develop　estimation　procedures　for　partially　linear　quantile　regression　models,　where　some　of　the　responses　are　censored　by　another　random　variable.　The　nonparametric　function　is　estimated　by　basis　function　approximations.　The　estimation　procedure　is　easy　to　implement　through　existing　weighted　quantile　regression,　and　it　requires　no　specification　of　the　error　distributions.　We　show　the　large-sample　properties　of　the　resulting　estimates,　the　proposed　estimator　of　the　regression　parameter　is　root-n　consistent　and　asymptotically　normal　and　the　estimator　of　the　functional　component　achieves　the　optimal　convergence　rate　of　the　nonparametric　function.　The　proposed　method　is　studied　via　simulations　and　illustrated　with　the　analysis　of　a　primary　biliary　cirrhosis　(BPC)　data.