The process of the Gaussian beam propagating through the nonlinear medium is calculated by step FFT,and the M² factor is get by minimizing the root-mean-square of the quadratic curve,the simulation results show: on the condition that the B integral is no more than 2,the stronger the Kerr effect is,and the bigger the M² factor is;and in which the beam width and the length between the waist plane and the nonlinear medium are two important factors on the influence between the Kerr effect and M² factor,namely the narrower beam width and the longer length are,the and the bigger the M² factors are.The compensation adopting the negative nonlinear refractive index medium to reduce the Kerr effect is studied and the beam quality is improved effectively. The both side compensation is selected as an idea method in the three types of methods.