Flow around a circular cylinder with different Reynolds numbers (Re is 80~1646) is numerically studied by using Granule Hydrodynamics Method (GHM), and the significant flow characteristics are gained. On the basis of actual simulation, the characters of GHM and the problems for further research are discussed. The GHM thinks the fluid as a discrete system, the fluid field in the system is made up by fluid granules, and the reasons for the fluid motion are fluid granule elastic collision and density difference (pressure difference). GHM has got the law of fluid motion based on the constitutive relation built by the equation of state, Pascal principle, and the speed equation of sound in the gaseous phase, however not based on the traditional Navier-Stokes equation. The fluid motion caused by the fluid granule elastic collision is determined based on the equation of state for fluids and their constitutive relation under the Hertzian contact theory, and the fluid motion caused by density difference is determined based on the Pascal principle and the speed equation of sound in the gaseous phase. GHM has given the physical properties of fluid and solid into consideration. There is a couple of symmetric vortex behind the cylinder, when the Reynolds number is between 5 and 40. When the Reynolds number is about 190, the couple of symmetric vortex is started breaking away from the cylinder. With the increase of Reynolds number, the flow behind the cylinder appears as different forms.