Parametric study of vortex generators (VGs) on the transonic infinite-wing with two types of airfoil is performed by using computational fluid dynamics (CFD) to identify the effects of five parameters: height, aspect ratio, incidence angle, spacing and chord location, on the aerodynamic characteristics. First, SC(2)-0518 airfoil with large thickness ratio and leading edge radius is employed. It becomes obvious that the VG spacing affects the shock wave location significantly. If the spacing is narrow, the shock wave is moved down stream, which increases the lift coefficient at high angle of attack. In contrast, the broad spacing suppresses the fluctuation of the pitching moment coefficients. This difference is caused by the interaction among vortices. The VG height changes the drag coefficients and is correlated with the VG spacing. The other airfoil considered is a cross-section airfoil of NASA common research model (CRM) with small thickness ratio and leading edge radius. The spacing effect with this airfoil is almost the same as that of SC(2)-0518 airfoil while it is revealed that VG is more effective for the airfoil easily stalling. The VG location has little influence, but VG located at more upstream will reduce the shock-induced separation up to larger angles of attack. Additionally, the appropriate incidence angle exists for generating the vortex most efficiently. This appropriate angle is determined by the vortex strength and the energy loss caused by VG. Finally, the aspect ratio controls the vortex strength. VG is not effective at all if the appropriate aspect ratio is not employed.