An X-band high gain and high efficiency triaxial relativistic klystron amplifier comprises a cathode holder 301, a cathode 302, an anode outer cylinder 303, an inner conductor 304, a modulation cavity305, a first reflection cavity 306, a first cluster cavity 307, a second reflection cavity 308, a second cluster cavity 309, a third reflection cavity 310, an extraction cavity 311, a cone waveguide312, a feedback loop 313, an electron collector 314, a support rod 315, a microwave output port 316, a solenoid magnetic field 317, and an injection waveguide 318, wherein the overall structure is rotationally symmetric about the central axis OZ axis. The amplifier, by rationally designing the electromagnetic structure of the device, overcomes the shortages such as complex structure, and relatively low gain (about 40 dB), efficiency (less than 30%) and output microwave power (about 1 GW) of axial injection or lateral dual-port injection in the existing X-band triaxial relativistic klystron amplifier, and realizes the high-gain, high-efficiency, and high-power microwave output of the triaxial relativistic klystron amplifier in the X-band.