Homogenerous nucleation process induced by the colored noise is simulated by the phase field crystal method. The results indicate that the noise strenghth within a certain range almost has no influence on the parameters of equilibrium thermodynamics of the nucleation system, such as nucleation engergy barrier and size of crtical nucleus; however, it will strongly affect the dynamics of the system. The incubation time of nucleation decreases exponenially with the increase of the noise strength. Further analysis shows that this is attributed to the fact that the colored noise can affect the atom mobility in the nucleation process.