The design of 10MeV/20kW high power irradiating accelerator is presented.The Backward-Traveling-Wave (BTW)accelerating structure is adopted.This structure combines the advantage of traveling-wave accelerator structure with low power reflection and high stability and standing-wave accelerator structure with high shunt impedance.The work frequency of this accelerator is 2856MHz.Designed by Code AccDesign which is coded by ourselves,the output electron beam with final energy 10MeV and peak current 300mA was reached.The length of the accelerating tube is 1.5m,and the power efficiency from microwave to electron beam is 66%.The temperature and stress distribution were simulated.And the frequency shift by microwave loss was calculated.