In　this　paper,　we　develop　statistical　inference　procedures　for　functional　quadratic　quantile　regression　model　in　which　the　response　is　a　scalar　and　the　predictor　is　a　random　function　defined　on　a　compact　set　of　R.　The　functional　coefficients　are　estimated　by　functional　principal　components.　The　asymptotic　properties　of　the　resulting　estimators　are　established　under　mild　conditions.　In　order　to　test　the　significance　of　the　nonlinear　term　in　the　model,　we　propose　a　rank　score　test　procedure.　The　asymptotic　properties　of　the　proposed　test　statistic　are　established.　The　proposed　method　provides　a　highly　efficient　and　robust　alternative　to　the　least　squares　method,　and　can　be　conveniently　implemented　using　existing　R　software　package.　Finally,　we　examine　the　performance　of　the　proposed　method　for　finite　sample　sizes　by　Monte　Carlo　simulation　studies　and　illustrate　it　with　a　real　data　example.