Graphene offers unique properties such that changing the incident energy density of the carriers by gate voltage leads to alteration of the chemical potential that can be used in light manipulation of photonic devices. In this work, we propose a band-stop filter hybrid graphene nanostructure composed of a graphene layer which is added to a metal–insulator–metal plasmonic waveguide structure. We use the finite element method to numerically calculate the light transmission of the graphene-based structure for adjusting chemical potential of graphene. Our calculations show that with constant structural parameters the observed transmission is modified when the chemical potential of graphene changes. Also, the transmission can be filtered in specific wavelength by controlling the chemical potential. The result shows the filtering at lower wavelengths by increasing the chemical potential. Moreover, the performance of this structure for the different channel width and refractive index of insulator is studied.