Abstract: The phase-locking properties of an S-band relativistic klystron amplifier (RKA) are investigated. In 2.5-dimensional particle-in-cell simulations, the influences of the electron beam voltage waveform on RKA phase-locking are studied. The results show that the spike in the voltage waveform of the electron beam has a positive effect on the RKA phase-locking properties, and it can reduce the time spent to achieve the locked state. A spike of 20% over the original voltage amplitude can cause a change of about 23 in the phase difference. Waveform flat-drops have negative impacts on the phase-locking of the RKA, which make the phase prematurely depart from the steady state. A flat-drop of 5% off the original voltage amplitude can cause a deviation of 50 in the phase difference. The rise time of the voltage waveform influences the RKA phase locked state either, but the trend is not obvious. The influence of the guiding magnetic fields on the phase is studied in a three-dimensional PIC simulation. The results show that the phase differences decrease when the guiding magnetic fields increase in the overall trend when the magnetic fields are below 1.6 T. In detail, the step form is shown, i.e. within a certain range, the changing of the guiding magnetic fields does not result in the changing of the phase differences. Experimental studies show that the phase differences decrease when the guiding magnetic fields increase. In the experiments, the guiding magnetic fields are between 0.6 T and 1.1 T, and the step form of the phase differences is not obvious.