Abstract: With the electromagnetic code, a frequency-tuned relativistic klystron amplifier (RKA) is designed and calculated. It is found that the operation frequency of the RKA can jump across S-band and C-band by adjusting the feeding frequency and the length of the output cavity. A 1 GW averaged power over the oscillator period is generated by simulation, with 700 kV electron beam voltage, 4 kA current, and 340 kW feeding power. The frequency of the output microwave is 3.2 GHz. The efficiency is about 35%. Meanwhile, a C-band microwave with a frequency of 5.6 GHz and a power level of above 490 MW is generated when the feeding frequency is 2.8 GHz and the output cavity length is 3.7 cm. The efficiency is about 17%.