In this Letter, we report on the structural and optical characteristics of ZnO films with a wurtzite structure grown on MgO (001) substrates with cubic structures. The ZnO films were prepared through the molecular beam epitaxy method, and growth orientation transformation from [0001] to [10-10] direction was observed with the change of growth temperature and thickness. The x-ray diffraction pole figures and in situ RHEED patterns demonstrated that the rotational relationship among grains within the ZnO films appeared in a typical two-fold rotation of about 30° for the [0001] growth orientation and four-fold rotation of about 30° or 60° for the [10-10] growth orientation, respectively. Last, we investigated their optical properties through measuring the transmission and photoluminescence spectra of the ZnO films, which showed the bulk-like bandgap feature of the ZnO films in spite of the existing growth orientation transformation.