In this study, a modulation instability (MI)-enhanced optical frequency comb generation (FCG) method is proposed on the platform of graphene-dielectric heterostructure included in a Fabry–Perot microresonator. The latter can provide the enhanced nonlinearity required for initiating and proceeding the MI procedure and leads to the generation of extra sidebands within the comb spectrum. In the first step, the influence of Fermi energy/feedback depth on the FCG process is investigated, considering that the MI mechanism merely interferes in the FCG process. Then, the combination of MI mechanism and electro-optical modulation is assumed as a hybrid method to explore the effects of modulation depth and modulation frequency. It is shown that a tooth spacing of about 0.49 GHz can be obtained while the linewidth is almost 0.8 MHz as the best result. Other important features are the adjustable tooth spacing due to the tuneable Fermi energy of graphene with a very low bias voltage (less than 1 V), low turn-on power of 11 µW and the amplification of optical power more than 95 dB which is in consequence of the MI-induced amplifying scheme. On this basis, the graphene-based electro-optical modulator working in the MI regime can be suggested for applications in atomic clocks and molecular fingerprinting for which precise measurements are needed using a terahertz frequency comb.