In　this　note　we　study　the　global　wellposedness　of　a　two-dimensional　incompressible　Navier-Stokes　fluid　structure　interaction(FSI)　model.　The　existence　and　unique-ness　of　the　global　strong　and　smooth　solution　to　the　initial　boundary　value　problem　for　one　class　of　the　FSI　model　in　the　two-dimensional　case,　which　is　one　model　of　two-dimensional　incompressible　Navier-Stokes　equations　coupled　by　the　two-dimensional　wave　equation　by　the　suitable　boundary　conditions　at　the　interface　boundary,　are　obtained　for　any　smooth　initial　data　under　the　assumption　of　the　suitable　compatibility　conditions　on　the　initial　data　at　the　interface　boundary　and　external　boundary　of　the　domain.　＇(c)　2022　Elsevier　Ltd.　All　rights　reserved.