Abstract: Phase characteristic is one of the key parameters which limit the promotional applications of intense relativistic klystron amplifier. In order to reduce the phase jitter and improve the stability of device, an S-band intense relativistic klystron amplifier (RKA) with three cavities and annular beams is studied theoretically. The theoretical results indicate that fluctuation of intense pulse, self-oscillation, non-uniform of beam emission and transmission are the main reasons for phase fluctuation. Then some optimization works are done as follows: (1) The structure of diode are optimized to improve the uniformity of electric beams; (2) Microwave absorbing materials are added in the drift to suppress the self-oscillation; (3) On the condition of output power greater than GW level, the parameters of cavities are optimized to reduce the phase jitter caused by fluctuation of pulse voltage. At last, an experiment research is carried out on the LTD accelerator to confirm the effectiveness of optimization. The experiment results show: on the condition of output power greater than GW level, the standard deviation of output microwave phase is about 10 within 100 ns in single shot and about 20in 5 Hz repeat. The phase difference jetter between two RKAs is about 20.