A new direction for high-power microwave (HPM) development is to investigate devices capable of producing HPMs with a complicated spectrum. In recent years, some HPM sources with two stable and separate frequencies have been investigated theoretically and experimentally. However, many short-comings still exist in these devices. Especially, the beam-wave interaction efficiency and the output microwave power are low in such devices. This paper proposes a novel dual-frequency HPM generator based on transition radiation. In the device, the electromagnetic fields are localized near the resonator cavities in the form of standing waves, and thus the interference between the different HPM components with different frequencies is weak. Compared with the existing dual-frequency devices, the new structure allows high beam-wave interaction efficiency and high output microwave power. As indicated in particle-in-cell simulation, with an electron beam of 500 kV voltage and 15.0 kA current guided by a magnetic field of 0.8 Tesla, an average power of 1.60 GW with a total power conversion efficiency of 21.3% is obtained, and the frequencies are 1.53 GHz and 3.29 GHz, respectively. Power level between two HPMs is comparable. The simulation results verify the feasibility of the dual-frequency HPM generator.