Abstract: The introduction of bunching cavities can significantly increase the gain of relativistic klystron amplifier, and correspondingly the power of the seeding microwave can be reduced to a very low level. Though higher gain can be obtained with more bunching cavities, the self-exciting problem will seriously disturb the working mode in the device. A special structure is introduced to deal with such problem. Based on the engineering requirement, a S-band of 3 GW relativistic klystron amplifier is designed with the seeding power 20 kW. In the simulation, the fundamental current modulation depth is 80% and the output microwave power reaches 3.3 GW with the seeding power of kilowatts.