The radiation pattern of an oversized waveguide horn typically changes considerably with frequency, which may result in waveform distortion when transmitting or receiving wideband signals. An approach for designing a broadband oversized waveguide horn with a stable radiation pattern is proposed by synthesizing a mixture beam. By analyzing the radiation characteristics of waveguide modes, a method is proposed for generating a mixture mode that varies with frequency to offset changes in radiation patterns caused by waveguide dispersion. To obtain the desired output modes over a broad bandwidth, a two-level optimization algorithm based on mode matching theory and particle swarm optimization (PSO) is developed. A smooth-wall oversized multimode horn is designed, fabricated, and validated via measurements. The measurement results indicate that the horn can output highly symmetric fields. The radiation patterns are highly consistent within +/- 8 degrees range, and the gain change is less than 0.4 dBi in the frequency range of 32-38 GHz. The frequency-invariant output of the horn contributes to the stable working of antennas, thus improving the efficiency of broadband high-power millimeter-wave systems.