Model　checking　methods　based　on　non-parametric　estimation　are　widely　used　because　of　their　tractable　limiting　null　distributions　and　being　sensitive　to　high-frequency　oscillation　alternative　models.　However,　this　kind　of　test　suffers　from　the　curse　of　dimensionality,　resulting　in　slow　convergence,　especially　for　functional　data　with　infinite　dimensional　features.　In　this　paper,　we　propose　an　adaptive-to-model　test　for　a　parametric　functional　single-index　model　by　using　the　orthogonality　of　residual　and　its　conditional　expectation.　The　test　achieves　model　adaptation　by　sufficient　dimension　reduction　which　utilizes　functional　sliced　inverse　regression.　This　test　procedure　can　be　easily　extended　to　other　non-parametric　test　methods.　Under　certain　conditions,　we　prove　the　asymptotic　properties　of　the　test　statistic　under　the　null　hypothesis,　fixed　alternative　hypothesis　and　local　alternative　hypothesis.　Simulations　show　that　our　test　has　better　performance　than　the　method　that　does　not　use　functional　sufficient　dimension　reduction.　An　analysis　of　COVID-19　data　verifies　our　conclusion.