Quasi-optical mode converters are usually used in gyrotrons to realize the conversion of high-order cavity mode to Gaussian beam. Using the scalar diffraction theory, the K-S phase-correcting optimization iterative algorithm Geometrical Optics and the least mean square(LMS) algorithm, this paper designs a dual-frequency quasi-optical mode converter with operating frequency of 105 GHz (TE_18,7) and 140 GHz (TE_24,9). According to the simulations results, the conversion efficiencies are 97.3% at 105 GHz and 99.0% at 140 GHz. And the Gaussian contents of the output beam on the window surface are 98.0% at 105 GHz and 99.7% at 140 GHz. This high efficiency dual-frequency quasi-optical mode converter can be used in a MW dual-frequency gyrotron.