This paper demonstrates improving method of asymmetric ground-plane cloak by applying unequally generated initial grids and compensating the notorious lateral shift of the ground-plane cloak. By generating initial grids unequally, broken grids of quasi-conformally mapped grids are corrected. Thus, an error of reflection angle of asymmetric ground-plane cloak is compensated. Moreover, by increasing the height of the bump and cloak, and shifting down the cloaking material below the reference ground plane, the lateral shift of the ground-plane cloak is compensated effectively. The proposed method is verified via the ray tracing simulation results using commercial software, the Comsol multiphysics.