Based on the Fresnel-Kirchhoff diffraction theory,the focusing property of the Gaussian beam transmitted through the thin Kerr medium is studied. The simulation for the phase-delay ranging from to is made,and the results show that,for medium with positive nonlinear refraction index,the Kerr effects of the beam may improve the focused peak intensity and the PIB on the focal plane,enlarge the relative focal shift and reduce the peak intensity on the geometry focal plane;but for negative index medium,it will reduce the focused peak intensity and its PIB on the focal plane,but other properties of the focusing remain the same as the positive one. And the influence of the Kerr effects on the focusing property can be reduced by enlarging the Fresnel number of the Gaussian beams.