Relaxation and local structure changes of a molten Cu135 cluster have been studied by molecular dynamics simulation using embedded atom method when the cluster is rapidly quenched to 700K, 600K, 500K, 400K, 300K, 200K, and 100K. With decreasing quenching temperature, details of energy evolvement and relaxation are analyzed. The simulation results show that the final structures are molten at 700K, like-icosahedral geometry at 600K-200K, non-crystal at 100K. The average energy of atoms is the lowest at 500K, and in the relaxation has abrupt increase at 25,135 and 42ps separately at 400K, 300K, and 200K. The simulation reveals that the quenching temperature has great affect on the relaxation processes of the Cu135 cluster after β relaxation region.