The magnetic anisotropy of sputter-deposited CoPt∕AlN multilayer films has been studied in contrast with the multilayer films consisting of magnetic and noble metals. It has been found that the as-deposited multilayer film shows enhanced in-plane magnetic anisotropy compared with CoPt alloy film of equivalent thickness. However, upon thermal annealing in a vacuum, the film undergoes a smooth transition of magnetic anisotropy from in-plane to perpendicular direction; moreover, the anisotropy field and coercivity can be controlled by controlling the annealing temperature. Structural characterization has revealed that the perpendicular magnetic anisotropy of the annealed CoPt∕AlN multilayer films is mainly of magnetoelastic origin.