A　new　algorithm　combining　nonlinear　Galerkin　method　and　coupling　method　of　finite　element　and　boundary　element　is　introduced　to　solve　the　exterior　nonstationary　Navier-Stokes　equations.　The　regularity　of　the　coupling　variational　formulation　and　the　convergence　of　the　approximate　solution　corresponding　to　the　algorithm　are　proved.　If　the　fine　mesh　h　is　choosed　as　coarse　mesh　H-sgure,　the　nonlinear　Galerkin　method,　nonlinearity　is　only　treated　on　the　coarse　grid　and　linearity　is　treated　on　the　fine　grid.　Hence,　the　new　algorithm　can　save　a　large　amount　of　computational　time.