This paper has analyzed the AM-AM and AM-PM characteristics of 7.9 GHz~8.4 GHz X-band TWT used for satellite communication and improved its linearity and IMD performance by using linearizer. The TWT amplifier with the linearizer shows better AM-AM and AM-PM conversion, and has increased 1 dB compression point by 12.3 dB and $2.0^{circ}/dB$ phase distortion point by 10 dB. The 3rd order intermodulation distortion, IMD3 is measured to be 37.0 dBc that is 16.2 dB improvement at the operating output. This paper also proposed the measurement method of IMD for high power amplifier, and that TWT amplifier can have better linearity and output power by compensating for the AM-PM characteristics.