X-ray free electron laser (XFEL) facility based on electron linear accelerator (LINAC) is regarded as one kind of the fourth-generation light source with the characteristics of high intensity, exceptional brightness, ultrashort pulse duration, and spatial coherence. In electron linear accelerator, energy of beam bunches is provided by high-power electromagnetic microwaves which are generated by a microwave tube called klystron. The stability of beam voltage of klystron occupies a key position in both the stability of output RF (Radio Frequency) power and the jitter of output RF phase, furthermore, it plays an extremely important role in beam energy stability of electron linear accelerator. In this paper, high power RF fluctuation and phase jitter of klystron output caused by beam voltage instability of klystron are analyzed and calculated. Influence of klystron beam voltage instability on beam energy gain in linear accelerator have also been further analyzed and calculated. The calculating procedure is particularly valuable for us to understand the relationship between pulse modulator stability and beam energy gain fluctuations. Finally, relevant experimental results measured by Shanghai Soft X-ray Free Electron Laser Test Facility (SXFEL-TF) is presented.