A multilayer waveguide window is demonstrated to exhibit wide bandwidth and high transmission for applications in high-frequency microwave tubes. A transfer matrix approach is employed to discretize the dielectric function profile of the multilayer heterostructure in a rectangular waveguide. The closed form has been obtained and the corresponding reflection and transmission characteristics have been carried out. The analytical calculation is also compared with the result of numerical simulation via the finite-element code HFSS. The exact calculation agrees with the numerical simulation very well. By comparison, the approach not only enhances the accuracy and efficiency, but also gives a good criterion for the design. The results show that the bandwidth for a transmission of 99%, i.e., S 11 below -20 dB, can be optimized to be about 8.75 GHz at a central frequency of 35 GHz or about 25%. A wide-bandwidth waveguide window can be easily designed for Ka-band and W-band tubes, and even for higher frequency ones.