In this paper, we proposed a graphene-silicon nitride (GSN) waveguide model, which was unveiled to unveil its second-order dispersion (SOD) characteristics. The influences of the different thicknesses of graphene layer and the different heights from graphene to the core material of silicon nitride on SOD were investigated in detail. The tunability of SOD via controlling the bias voltage applied to the graphene layer was demonstrated and a 50 nm wavelength tuning was achieved with a small perturbation in voltage while keeping the geometric structure of the waveguide unchanged. Moreover, a flat SOD curve of the GSN waveguide was obtained with a large bandwidth of 700 nm between the two zero-dispersion wavelengths (ZDWs). These results provided significant insights for potential applications of graphene-related optoelectronic devices, integrated optics, and optical communications.