We measure the phase fluctuation in a high-power fiber amplifier using a multi-dithering technique. Its fluctuation property is qualitatively analyzed by the power spectral density and integrated spectral density. Low frequency fluctuations caused by the environment are dominant in the phase fluctuations in an amplifier, whereas the high frequency components related to laser power affect the control bandwidth. The bandwidth requirement of the active phase-locking is calculated to be 300 Hz, 670 Hz, 1.6 kHz, and 3.9 kHz under the output power of 25, 55, 125, and 180 W, respectively. The approximately linear relationship between the control bandwidth and laser power needs to be further investigated.