Molecular dynamics (MD) simulations were used to study the diffusion activities of Cu atoms in supercooled state and amorphous state. The embedded atomic (EAM) potential was selected as many-body interaction. Using the mean square displacement (MSD), the diffusion properties of Cu atoms were investigated during relaxation. The transformations of microstructure feature were pursued by means of pair correlation function and pair analysis technique. The calculated results indicate that the diffusion of atoms plays an important role on the crystallization of liquid and amorphous Cu.