Interval-valued　functional　data,　a　new　type　of　data　in　symbolic　data　analysis,　depicts　the　characteristics　of　a　variety　of　big　data　and　has　drawn　the　attention　of　many　researchers.　Mean　regression　is　one　of　the　important　methods　for　analyzing　interval-valued　functional　data.　However,　this　method　is　sensitive　to　outliers　and　may　lead　to　unreliable　results.　As　an　important　complement　to　mean　regression,　this　paper　proposes　an　interval-valued　scalar-on-function　linear　quantile　regression　model.　Specifically,　we　constructed　two　linear　quantile　regression　models　for　the　interval-valued　response　and　interval-valued　functional　regressors　based　on　the　bivariate　center　and　radius　method.　The　proposed　model　is　more　robust　and　efficient　than　mean　regression　methods　when　the　data　contain　outliers　as　well　as　the　error　does　not　follow　the　normal　distribution.　Numerical　simulations　and　real　data　analysis　of　a　climate　dataset　demonstrate　the　effectiveness　and　superiority　of　the　proposed　method　over　the　existing　methods.