Using particle in cell simulation codes, a low radio frequency (rf) power driven relativistic klystron amplifier is designed according to the beam with current of 7.5 kA and voltage of 750 kV with special measures to avoid the mode competition. Simulated power reaches 1.7 GW when the driven rf power is 7.0 kW, the corresponding gain is 53.9 dB. Also the experiment is carried out on a telsa-typed accelerator, whose beam is with current of 8 kA and voltage of 800 kV. The measured rf output power reaches 2.04 GW in the experiment when the input rf power is 62 kW and frequency 2.850 GHz, the corresponding gain is 45.1 dB and efficiency is 32%. The maximum gain reaches 46.7 dB when the input decreases to 39 kW, the corresponding output rf power is 1.84 GW.