We calculate the free energy of an AB diblock copolymer thin film of cylindrical morphology under confined geometry and find that the size of the cylinder can be asymmetric, depending on the film thickness and surface tension. The size of the cylinder right above the surface is slightly smaller than that of the other cylinders. The equilibrium period in this thin film is different from that in the bulk because of the surface effect. The tendency toward asymmetry diminishes as the film thickness increases and the interfacial tension between the major block (A) and the substrate decreases.