RF phase Jitter is a very important parameter for a relativistic klystron amplifier, and it is closely related with the physical processes in the klystron. In view of the physical process in the klystron, the RF phase jitter is theoretically studied together with particle in cell （PIC） simulation. The main factor which affects the RF phase jitter is deduced and verified in the PIC simulation. The RF phase jitter is significantly affected by the fluctuation of the beam voltage at the steady state when the cavity is in resonanec. The relation is linear in a certain range.