Structural changes of a Cu13 cluster supported on a Cu（001） surface at low temperatures of 10 and 50 K are investigated through molecular dynamics simulations with using interatomic potentials from embedded atom method presented by Johnson. The calculations of atom density profiles show that the cohesive energy is affected mainly by the number and the configuration of the atoms which are directly contacted with the Cu（001） surface, as well as some different configurations of the atoms at higher positions. At 10 K, the initial position of the supported cluster has a larger effect on the atomic packing and the binding energy of cluster.