Epitaxial thin films of La₂CuSnO₆ have been grown on (001)-oriented SrTiO₃ substrates by a pulsed laser deposition method. The obtained films had the layered arrangement of Cu²⁺ and Sn⁴⁺ ions and also the 2-fold superstructure within the ab plane making a 2a×2a×2c tetragonal double-perovskite unit cell. Analysis of the interface between the La₂CuSnO₆ film and the SrTiO₃ substrate has revealed that the first B-site cation of the prepared La₂CuSnO₆ film is Cu. We have also succeeded in controlling the Cu/Sn ordering in the perovskite structure by changing the deposition temperature. The dielectric constant of the layered thin film is as twice as that of the random film suggesting the large anisotropic dielectric property of La₂CuSnO₆.