Abstract: In the triaxial relativistic klystron amplifier(TRKA), the mode leakage and the higher order parasitic mode self-oscillation seriously degrade klystron performance, cause pulse shortening. The electric field of the higher mode is explored in the PIC simulation, the higher mode in resonant cavity is proved to be TM21 mode, which is transformed into TE21 mode in coaxial drift tube. And the microwave attenuating material is introduced to suppress higher mode self-oscillation, the relations of the attenuating characteristics with electric conductivity, thickness and length of the attenuating material are studied. Then three dimensional simulation of the X-band TRKA with attenuating material is carried out, and the results show that the introduction of proper microwave attenuating material can well supress higher mode self-oscillation. We obtain a microwave with power of 1.1GW, efficiency of 37%, and gain of 42dB by simulation.