An S-band cylindrical cavity works on TM610 higher-order mode was designed on the basis of electromagnetic theory. Electromagnetic field distribution, frequency and mode spacing of TM610 mode and its adjacent modes were calculated by using HFSS, ISFELD3D, MAFIA and CST-MS. Simulation results indicate that the electromagnetic field of TM610 mode distributes in the section around drift tube, and there is no electromagnetic field in the center of the cavity. A ferrite RF absorber was set in the center of the cavity to suppress the non-work modes based on the characteristic of TM610 mode. Simulation results of HFSS show that most non-work modes are eliminated by RF absorber except the TM510 mode. An absorption cavity coupled to the main cavity was used to suppress the TM510 mode. Simulation re