We propose a theoretical scheme to improve the fundamental mode energy proportion of the supercontinuum (SC) generation in graded-index multimode fiber (GRIN-MMF). With this scheme, we conduct numerical investigations into the influence of various core refractive index profile parameters on beam-self cleaning of fundamental mode, establishing an optimal parameter range (α=2.0∼2.06). Within this range, the energy proportion of the fundamental mode gradually increases from 32% to 65% as the propagation distance. Additionally, our simulation provides the initial demonstration that the supercontinuum (SC) broadening is correlated with the distribution of core refractive indices within the graded-index multimode fiber.