We numerically calculated the coherence properties of the supercontinuum based on the definition of complex degree of mutual coherence, and obtained the spectral broadening of the pump pulse and the coherence properties of the generated supercontinuum under different pump powers. The results showed that the dominant underlying mechanisms of the spectral broadening are soliton self-frequency shift and dispersive wave generation when the pump wavelength located in the anomalous dispersion region of photonic crystal fiber. While the coherence properties are affected by the modulation instability which amplifies the stochastic noise of the pump pulse, thus the generated frequency components have stochastic phases and amplitudes, which induces the degradation of the coherence of the supercontinuum. The gain of modulation instability increases with the increasing of the pump power, and the effect of the noise on the supercontinuum will become greater which degrades the coherence properties. Low pump power is required to obtain high coherent supercontinuum, and suitable pump power should be adjusted to get wide bandwidth and high coherent supercontinuum.