Based on the fundamental principles of quasi-optical and Gaussian beams, research has been conducted on quasi-optical reflectors and lenses, leading to the design of a quasi-optical feed system for millimeter-wave and submillimeter-wave antennas. This system is capable of simultaneously receiving electromagnetic radiation signals in the 89~115 GHz and 176~183 GHz frequency bands through two optical paths. Elliptical reflectors and lenses are utilized to focus the beams and control the system's structural envelope. Polarization grid networks are employed to separate channels, and calculations and preliminary analysis of dual-channel performance are conducted. The system operates in a low-temperature environment, and in response to practical requirements and cold optical analysis, constraints are proposed and optimized for the spatial position and beam radius of quasi-optical components. Theoretical calculations and simulation results indicate that the system meets the design requirements for cold optics and quasi-optics.