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Complex magnetically insulated transmission line oscillator(MILO),as an important development direction,can enhance the power efficiency and generate dual-band high power microwaves(HPMs).A complex MILO and a preliminary dual-band radiation system have been proposed in our previous studies.However,the axial length of the dual-band radiation system is too long to meet the compact requirements.In this paper,a compact dual-band radiation system is presented and investigated numerically.The compact dual-band radiation system comprises a dual-band cross-shaped mode converter and a dual-band coaxial conical horn antenna.It can convert two coaxial TEM mode microwaves(1.717 GHz and 4.167 GHz)generated by the complex MILO into the coaxial TE11 mode microwaves,and then radiate them into the air.At 1.717 GHz,the gain of the antenna is 17.9 dB,and the total return loss and diffraction loss are 1.50％ and 0,respectively.At 4.167 GHz,the gain is 19.4 dB,and the total return loss and diffraction loss are 1.17％ and 0.78％,respectively.The power handling capacity of the antenna is 5.1 GW at 1.717 GHz and 2.0 GW at 4.167 GHz.Comparing with the original structure,the length of the dual-band radiation system is reduced by 45.2％.