The quasi-optical feed system is a key component of the millimeter/sub-millimeter sensor. The design theory and methods of millimeter/sub-millimeter wave quasi-optical system are described. The varieties, functions and design process of quasi-optical passive devices are generalized. Then, the quasi-optical feed systems, which can realize the dual-polarized receiving and dual-mode composite operation, are constructed and the working principles are also given in detail. Ultimately, the corresponding millimeter-wave dual-reflector antenna is obtained through simulation and optimization, and the whole system with subreflector fixed and main reflector scanning is able to realize ±10°airspace coverage.