Relaxation and local structure changes of a molten Cu57 cluster during rapidly quenching have been studied by molecular dynamics simulation using embedded atom method. With decreasing quenching temperature, atom motion details are analyzed using three factors, including the mean square displacement, incoherent intermediate scattering function, and non-Gaussian parameter, while the local structure changes are identified by pair analysis. Simulation results reveal that after a drastic collective motion of atoms, the temperature greatly affects the relaxation processes of the cooled cluster. At a high quenching temperature, after atoms dramatically move in a β relaxation region, diffusion motion of the atoms plays a dominant roles followed by non-diffusion rearrangements of local atomic structures, and no nucleation occurs. When the temperature decreases, local structure changes of atoms occur as the initial dramatic motion, then through the diffusion of atoms in the α relaxation region, and some unstable icosahedral structures are observed. At a low quenching temperature, the structure changes in the α relaxation region result mainly from non-diffusion rearrangement of the atom positions, and a notable amount of icosahedral structures are formed.