Abstract: The phase characteristic of multiple beams relativistic klystron amplifier is an important parameter, which limits the amplifiers applications. In order to reduce the phase jitter and improve the stability of the device, the phase characteristics of intense relativistic klystron amplifier is studied by one dimension non-linear theory. The theoretical results indicate that multiple frequency in the cavity and velocity gradient of electron beams caused by the characteristics of intense pulse voltage are the main reasons leading to phase fluctuation. Then numerical analysis of phase jitter caused by intense pulse power are developed based on an X-band multiple beam relativistic klystron amplifier with 18 electron beams. The theoretical and simulation results show together that front edge and fluctuation of pulse voltage both can lead to frequency shift and phase jitter. And the shift of operation frequency and fluctuation of phase will be greater while the rise time of pulse voltage is shorter. Besides, the shift of operation frequency is only determined by the fluctuation gradient of pulse voltage and the fluctuation of phase is determined by the fluctuation amplifier and gradient of pulse voltage.