Optical dispersion is associated with various nonlinear phenomena. If the dispersion characteristics of a waveguide can be actively tuned, nonlinear phenomena can be actively controlled on a single chip. In this study, we developed a new platform to actively control dispersion by controlling the absorption of graphene by adjusting the Fermi energy of graphene, a representative two-dimensional material. Based on this platform, we simulated whether it is possible to actively control the wavelength of dispersive waves generated by supercontinuum light, and obtained a control range of 180 nm. We also presented an novel method to reduce the high light absorption of graphene and further increase the control range. This could be utilized in a variety of fields, including spectroscopic applications.