Three dimensional numerical calculation carried out to investigate the eccentricity effect of intake valve on the in-cylinder flow fields for the intake stroke and the compression stroke. During the intake stroke, a corner vortex in the vicinity of the valve exit interacted strongly with a toroidal vortex in the case of axisymmetric valve. But a weak interaction between the corner vortex and the toroidal vortex occurred due to the eccentricity of the valve in the narrow region between valve and cylinder wall in the case of offset valve. During the compression stroke, it was found that a solid body rotation was maintained in the radial-circumferential plane in the case of axisymmetric valve. But a weak secondary vortex was formed in the radial-circumferntial plane in the case of offset valve, because of the interaction between swirl flows and inward flows towards cylinder axis. The calculated turbulence intensity presented a similar trend with the experiental results but, in spite of using the modified k-.epsilon. model, it was found that the qualitative difference between the numerical results and experimental results was large in the region where the velocity gradient is substantial.