A Fourier pseudospectral-finite difference scheme is proposed for unsteady Navier-Stokes equation. It is showed that the numerical solution keeps semi-discrete con-servation. The strict error estimation is established. The numerical results are presented A Fourier pseudospectral-finite difference scheme is proposed for unsteady Navier-Stokes equation. It is showed that the numerical solution keeps semi-discrete con-servation. The strict error estimation is established. The numerical results are presented