Abstract: In general case,super-Gaussian beam is not the solutions of Helmholtz equation and approximation condition of SVA.But,by means of varying the distribution of refractive index of transmitting medium,super-Gaussian beam could be the eigensolutions of Helmholtz equation.This paper proved that super-Gaussian beam is the eigensolution of wave equation in GRIN fiber, and derived the distribution function of refractive index.As the special examples of this paper,the cases of literature 3 and power law refractive index distribution are discussed.