A new theoretical model is suggested for gyro-electric cylindrical waveguides incorporating graphene layers in this article. To validate the model, the analytical result of FOM is compared to simulation one prepared by COMSOL for a graphene nano-wire. The full agreement between them is seen, which confirmed the high accuracy of our model. As a special case of the general waveguide, a novel gyro-electric-based waveguide with double-layer graphene, constituting graphene-InSb-graphene-SiO2-Si layers, is introduced and investigated. It is shown that the FOM of the designed waveguide could be altered via the chemical potential and the magnetic field.