The coherence properties of the supercontinuum generated by a picosecond pulse in normal dispersion region of highly nonlinear fiber are numerically calculated and analyzed at different input noise powers by introducing the definition of the complex degree of mutual coherence. The results show that the coherence of the generated supercontinuum is affected by the noise ratio of the picosecond pulse. The coherence of the spectrum sidelobes generated by optical wave breaking is lower than that of the center part of the spectrum. The chirp of pulse and shape of pulse do not have an obvious effect on the coherence of the broaden spectrum. Low noise power input is required to obtain high coherent supercontinuum, and the pump power and waveshape should be optimized to obtain the wide bandwidth and high coherent supercontinuum.