In order to realize the combination of the coherent high power microwave, an S-band high gain relativistic klystron amplifier with high phase stability is presented and studied theoretically and experimentally. The phase characteristics of the output microwave are explored in particle-in-cell code and experiment. The experimental results accord well with the simulation results, which indicates that the parasitic oscillation excited by retrograde electrons is the main cause of phase variation in the development of high-gain relativistic klystron with high phase stability. When the input RF power is 10 kW, a microwave pulse with about ± 10° in relative phase difference fluctuation between output and input is obtained in experiment. And the corresponding locking duration is about 90 ns. Accordingly, the expectation of power combination efficiency of 10 high-gain relativistic klystron amplifiers can be achieved to be 99% with continuous uniform distribution of random relative phase difference.