High-quality ZnO films have been grown on epi-GaN predeposited on Al2O3 substrates using RF-plasma assisted molecular beam epitaxy. The growth conditions to obtain high-quality ZnO films on epi-GaN are Zn-pre-growth treatment on epi-GaN and two-step growth. RHEED intensity oscillations are observed from the beginning of ZnO growth on the low-temperature ZnO buffer layer indicative of two-dimensional growth. Low-temperature (10 K) photoluminescence of ZnO films grown on epi-GaN shows that the linewidth of the strongest emission at 3.3676 eV is as narrow as 1.5 meV, while the deep-level emission at around 2.3 eV is negligibly small.