Imputing　missing　values　in　multivariate　spatial–temporal　data　is　important　in　many　fields.　Existing　low　rank　tensor　learning　methods　are　popular　for　handling　this　task　but　are　sensitive　to　high　level　of　skewness.　The　aim　of　this　paper　is　to　develop　an　alternative　method　with　robustness　and　high　imputation　accuracy　for　multivariate　spatial–temporal　data.　In　view　of　the　fact　that　quantile　regression　is　robust　to　noises　and　outliers,　we　propose　an　imputed　quantile　vector　autoregressive　(IQVAR)　model.　IQVAR　can　simultaneously　impute　missing　values　and　estimate　parameters　of　quantile　vector　autoregressive　model.　The　objective　function　includes　check　loss　and　nuclear　norm　penalization.　We　develop　an　ADMM　(Alternating　Direction　Method　of　Multipliers)　algorithm　to　solve　the　resulting　optimization　problem.　Simulation　studies　and　real　data　analysis　are　conducted　to　verify　the　efficiency　of　IQVAR.　Compared　with　other　approaches,　IQVAR　is　more　robust　and　accurate.　©　2024　Wiley　Periodicals　LLC.