Si $_3$ N $_4$ has emerged as a prominent material for expanding the capability of silicon photonics to wavelengths below $ $\mu$ m. However, realizing an efficient optical modulator, a key building block for any integrated optics platform, remains a major challenge in Si $_3$ N $_4$ mainly because this material has a vanishing Pockels coefficient. Here, we propose a compact Si $_3$ N $_4$ based optical modulator by using a thin VO $_2$ layer on top of a Si $_3$ N $_4$ strip waveguide where amplitude modulation is achieved via phase transition of the VO $_2$ layer. To reduce the actuation time of the temperature-induced VO $_2$ phase transition, a mono-layer graphene microheater is designed for the active Si $_3$ N $_4$ VO $_2$ waveguide. Our simulations indicate a high extinction ratio of $\sim$ 8.28 dB/ $\mu$ m with an insertion loss of $\sim$ 2.8 dB/ $\mu$ m at the design wavelength of 850 nm for the proposed modulator and wideband operation in the wavelength range of 800–900 nm. It is shown that employing the electrical and thermal properties of graphene not only leads to a significant reduction of the power consumption of the device but also, decreases the actuation time compared to previous modulators based on the thermal phase transition of the VO $_2$ .