Abstract: The simulation of incompressible fluid past a circular cylinder of diameter D at moderate Reynolds number on the basis of full unsteady Nnvier-Stokes equation is accomplished by a new method described in this paper. The cylinder is started impulsively with a constant velocity. Reynolds number(Re=U∞D/v)was chosen as 200,550 and 3000 respectively. We obtained numerically the non-steady flow near cylinder and the formation of isolated secondary eddy and secondary eddy pair. Furthermore, the numerical results are agreement with recent experimental results. The method presented here is a sequel to elliptic-vortex method prese nted-by Zhen-huan Teng in [1]. In the paper we allow the change of shape of vortices from ellipic as it locates near cylinder and then circular far from cylinder. We intend to simulate flow separation based on Navier-Stoke equation instead of P-rantl's equation. The fulfillment of boundary condition on the surface of the cyli-nder is crucial. We compare various reasonable numerical treatment of this kind of boundary condition, and present in detail the best one.