Abstract: Based on the Fresnel-Kirchhoff diffraction theory,the focusing property of the one-dimension super-Gaussian beam transmitted through the thin Kerr medium is studied.The simulation for the phase-delay ranging-2rad~2rad is made,and the results show that,for the medium with positive nonlinear refraction index,the Kerr effect of the beam improves the focused intensity,broadens the relative focal shift and reduces the peak intensity on the geometry focal plane;but for negative index medium,it will reduce the focused intensity,however,the other focusing properties remain the same as the positive one.Both conditions can be discussed together,and the influence of the Kerr effect on the focusing property can be reduced by enlarging the beam Fresnel number.