A novel sub-micron optical waveguide based on silicon-on-germanium (Ge-on-Si,GOS) was proposed and by adjusting second-order dispersion curves the waveguide structure were optimized and designed .Then this article studied its wavelength conversion properties between 3 μm and 6 μm.The numerical results show that this waveguide can achieve high conversion efficiency in broadband infrared wavelength conversion when the pump light wavelength near the zero dispersion point at negative wavelength region of the second-order dispersion curves at the optimized waveguide structure which the ridge width is 2.8 μm,ridge high is 1.6 μm and slab thickness is 0.48 μm.The 3 dB conversion bandwidth reaches 1664 nm and the maximum conversion efficiency can reach -2.479 dB at the 0.05 GW/cm2 power density of the pump light .This waveguide has potential applications in terms of future photonic networks and communications space due to its large wavelength conversion bandwidth and high conversion efficiency advantages.