The depositing process of (Cu)13 cluster, on Cu(001) surface with icosahedral structure and en-ergy ranging from 5 to 20 eV per atom, is investigated by molecular-dynamics simulations. A many-body hybrid potential, which is a combination of the tight-binding with Moliere potential, is used. The dynamic behavior of deposition is studied by taking the "snapshots" of cluster-substrate interac-tion. It is found that the cluster atoms rearrange and form epitaxial layers on the surface without cre-ating point defects after full relaxation at low energy. A clear trend of deeper penetration of the clus-ter atoms into the substrate with increasing energy is observed. A cluster with energy 20 eV per atom completely embeds itself inside the substrate while creating radiation damage. Energy analyses show that the cluster atoms activate the substrate atoms in impact regjon through collective collisions in a very short time (some tenth picoseconds), and provide energies for the migration and reconstruction of atoms.