Direct numerical simulations (DNS) of flows around a two-dimensional cylinder with Re=56, 140 and 226 by the higher-order finite difference scheme (FDS) have been conducted. A newly constructed outflow boundary condition, which has been successfully tested on a spatially developing mixing-layer has been applied. Various comparisons of relevant flow properties like drag coefficient, Strouhal number and the length of the formation region with experimental data are performed. In addition, the adequacy of the resultant flowfield both in the formation and the stable region has been investigated in terms of the decay of the vorticity and the velocity fluctuation. From these studies, the following conclusions are obtained. (1) In the formation region, the decay of the shed vortex obtained by DNS shows good agreement with the experimental result as to peak values of vorticity. The shear stress field obtained by DNS shows a concentrated region of shear stress at the moment of vortex shedding, which is observed in the experimental results. (2) In the stable region, the decay of the velocity fluctuation obtained by the present DNS shows good agreement with the experimental results. (3) In the Reynolds number region below Re=226, global properties describing the wake behind the cylinder such as the length of the formation region and the strength of the vortices obtained by the DNS show good agreement with the experimental results.