An X-band coaxial multi-beam relativistic klystron amplifier is designed in order to increase output microwave power and operating frequency of the amplifier tube. The experiment is performed on a Tesla-type accelerator. The amplifier is driven by an electron beam of 2.8 kA at 720 kV, and a microwave power of 30 kW and frequency of 9.384 GHz is injected into an input cavity by means of an external source, then a microwave power of over 800 MW is extracted, the amplifier gain is about 44 dB, and conversion efficiency is 40%. The experiment proves that output power of nearly GWs can be generated with the X-band coaxial multi-beam relativistic klystron amplifier driven by a kW-level input power. V C 2013 AIP Publishing LLC. [http://dx.