the dispersion profiles of a hybrid graphene-silicon (hygs) slot waveguide with trilayers of graphene are investigated in this paper. by tuning the bias voltage on graphene layer, the zero dispersion wavelengths (zdw) of hygs slot waveguide can be tailored dynamically and effectively. with small disturbed voltage (6 v), a large zdw tuning amount (200 nm) is achieved, without the need for changing the geometric structure of the waveguide, which has been verified with numerical simulation. moreover, the dispersion curve of hygs slot waveguide is flat enough (group velocity dispersion slope less than 2 ps/nm(2).km), in the vicinity of zdw. this waveguide is highly beneficial to such applications as integrated optics and graphene-related active optical devices.