Based on the nonlinear Schrödinger equation, the step FFT is used to simulate the propagation of the square super-Gaussian beam in Kerr medium, and the evolution characteristics of the axial center and diagonal intensity of the square super-Gaussian beam are analyzed. At the same time, the self-focusing characteristics, the variation of peak intensity and B-integral in Kerr medium are also analyzed. The research results show that after the square super-Gaussian beam passes through the Kerr medium, there are different degrees of intensity enhancement and depression at different distances from the center of the beam, the intensity enhancement and depression are weak near the beam center, strong at the edge and four corners of the beam, and they are stronger in the diagonal direction than in the axial center direction. Reducing the order can slow down the edge intensity enhancement of the beam and the growth of the B-integral. Reducing the thickness of the Kerr medium can reduce the intensity enhancement of the beam edge and the size of the B-integral. It is proposed that the main reason for the fluctuation of the edge intensity of the beam probably be the coherent superposition of the beam.