Preparation of the single crystal-like thin films of zinc oxide (ZnO), which is expected to be a next generation semiconductor, is usually studied using sapphire substrates because there is no other appropriate oxide substrate that has the same hexagonal crystal structure as ZnO. Here we study the fabrication of ZnO films on the ( I I I) plane of cubic crystals such as (LaAlO3)(0.3)(Sr0.5Ta0.5O3)(0.7) (LSAT) which have the same C-6 symmetry as ZnO, since film preparation on substrates is involved in developing opto-electronic devices. By using pulsed laser ablation deposition, high quality ZnO(0001) epitaxial films were fabricated on the cubic(111) substrate plane as well as the sapphire(0001) plane. These have a band gap of similar to 3.25 eV and high electric-resistivity of over 0.40 Omega-cm, and show a high optical transmittance of over 85% in the near ultraviolet and visible region. Those are fundamental characteristics for the starting matrix in developing wide band gap semiconductors by hole and electron doping.