Three-dimensional numerical simulations on the laminar flow around a circular cylinder with different diameter along the spanwise leading to a type of sinusoidal waviness, named wavy cylinder are performed at low Reynolds number. A series of wavy cylinders with different combinations of spanwise wavelength and wave amplitude are conducted at a Reynolds number of 100. The optimal range of wavelength and the effect of wave amplitude are obtained. The results show that the 3-D free shear layers from the cylinder are more difficult to roll up to vortex and hence the wake formation lengths of some typical wavy cylinders are larger than that of the circular cylinder and in some cases the free shear layers even do not roll up into vortex behind the cylinder. The mean drag coefficients of the typical wavy cylinders are less than that of a corresponding circular cylinder with the same mean diameter; also the fluctuating lift coefficients are reduced. The reduction of mean drag coefficient and fluctuating lift coefficient of wavy cylinder increases with the value of wavy amplitude. Furthermore, a typical wavy cylinder model at Re=150 is also simulated and found that the control of flow induced vibration by modifing the spanwise wavelength of cylinder has a relationship with the variation of Reynolds number.