The melting and freezing processes of CuN (N = 180, 256, 360, 408, 500, 628 and 736) nanoclusters are simulated by using micro-canonical molecular dynamics simulation technique. The potential energies and the heat capacities as a function of temperature are obtained. The results reveal that the melting and freezing points increase almost linearly with the atom number in the cluster increasing. All copper nanoclusters have negative heat capacity around the melting and freezing points, and hysteresis effect in the melting/freezing transition is derived in CuN nanoclusters for the first time.