The laminar and turbulent flows past an axisymmetric body with a ring wing were investigated numerically at various attack angles (0°-20°) for the Reynolds numbers ranging from 103 to 107. The DDM (Domain Decomposition Method) with the Schwarz iterative method based on finite difference approximation was applied to simulate this problem. The primitive variable formulation was used for the solution of the incompressible Navier-Stoke equations. The velocity field was calculated from the unsteady momentum equation by marching in time. The continuity equation was replaced by a Poisson-type equation for the pressure with the Neumann boundary conditions. The Baldwin-Lomax model was adopted to simulate turbulence effect. The leap frog implicit iterative method was used for the time difference approximations. The computed pressure at the front stagnation point is found to have a small deviation, less than 10%, from the theoretical value. The outlet flux has a loss about 5%. The lift coefficients increase linearly with the attack angle, but for attack angles greater than 15° the lift coefficients show mild decrease. The friction drag coefficients are insensitive to the attack angles, but the pressure drag coefficients increase markedly with the attack angles. In addition, complex flow patts are revealed within the vicinity of the ring wing.