Electro–optic modulator is a key component for on-chip optical signal processing. An electro–optic phase modulator based on multilayer graphene embedded in silicon nitride waveguide is demonstrated to fulfill low-power operation. Finite element method is adopted to investigate the interaction enhancement between the graphene flake and the optical mode. The impact of multilayer graphene on the performance of phase modulator is studied comprehensively. Simulation results show that the modulation efficiency improves with the increment of graphene layer number, as well as the modulation length. The 3-dB bandwidth of around 48 GHz is independent of graphene layer number and length. Compared to modulator with two- or four-layer graphene, the six-layer graphene/silicon nitride waveguide modulator can realize π phase shift at a low-power consumption of 14 fJ/bit when the modulation length is 240 μm.