Abstract: Traditional gyrotron quasi-optical mode converters are limited by single-frequency operating characteristics, which makes it difficult to meet the development needs of multi-frequency gyrotrons in the fields of fusion reactor heating and terahertz communication. In this paper, a design method for the quasi-optical launcher, supporting dual-frequency operation at 170 GHz TE_31,8 and 218 GHz TE_40,10, is proposed based on coupled-mode theory. It achieves dual-frequency operation within the same radiation aperture by optimizing the mode coupling parameters. By combining the new phase correction algorithm, the three-stage quasi-optical mirror system is constructed to realize the beam-electron beam trajectory separation and beam phase compensation. The simulated results show that the dual-frequency launcher achieves scalar Gaussian contents of 99.4% and 99.1% at the radiation aperture at 170 GHz and 218 GHz, respectively. After optimization by the mirror system, the radiation beam achieves scalar Gaussian contents of 99.0% and 98.9% at 170 GHz and 218 GHz, respectively. This paper realizes the collaborative design of the dual-frequency quasi-optical mode converter, which provides key technical support for the development of multi-frequency gyrotrons and has important engineering applications.