We propose a new strip/slot hybrid waveguide with double slots, which exhibits a flat and low dispersion over a 1098-nm bandwidth with four zero-dispersion wavelengths. Dispersion of dual-slot silicon waveguide is mainly determined by mode transition from a strip mode to a slot mode rather than by material dispersion. Dispersion tailoring is investigated by tuning different structural parameters of waveguides. Moreover, nonlinear coefficient of dual-slot silicon waveguide and phase-matching condition in FWM are both explored in detail. The dual-slot waveguide can be used to generate supercontinuum with bandwidth extending up to 1630 nm pumped by femtosecond pulses. This waveguide will have a great potential for ultrabroadband signal processing applications from near-infrared region to mid-infrared region.