Modern　spatial　temporal　data　are　collected　from　sensor　networks.　Missing　data　problems　are　common　for　this　kind　of　data.　Making　robust　and　accurate　imputation　is　important　in　many　applications.　There　are　complex　correlations　in　both　spatial　and　temporal　dimensions.　Thus,　it　is　even　a　challenge　to　model　missing　spatial-temporal　data.　In　this　article,　the　imputation　of　missing　values　is　with　the　help　of　related　covariates.　First,　we　transform　the　original　sensor　×　time　observational　matrix　to　a　high　order　tensor　by　adding　an　extra　temporal　dimension.　Then　we　integrate　quantile　tensor　regression　with　tensor　completion.　The　objective　function　includes　check　loss　and　nuclear　norm　penalty.　An　alternating　update　algorithm　combined　with　alternating　direction　method　of　multipliers　(ADMM)　is　developed　to　solve　the　objective　function.　Theoretical　properties　of　the　proposed　estimator　are　investigated.　Simulation　studies　show　our　proposed　method　is　more　robust　and　can　get　more　accurate　imputation　results.　Real　data　analysis　about　Beijing＇s　PM2.5　concentration　level　is　conducted　to　verify　the　efficiency　of　the　estimation　procedure.　©　2023　Elsevier　B.V.