Europium (Eu) and dysprosium (Dy) co-doped strontium aluminate (SrAl2O4) (SA:Eu, Dy) is one of the most widely applied long persistent phosphors due to its strong emission intensity and long afterglow. However, the difficulty to get crystalline SA:Eu, Dy thin films in the as-deposited state strongly limited their applications in devices and surface coatings. In this study, we present a breakthrough in the synthesis of single-crystal SA:Eu, Dy films via direct-epitaxial growth on sapphire substrate by means of pulsed layer deposition. A threshold temperature of 900 degrees C is identified, only above which the mobility of adatoms is high enough to form crystalline films. By avoiding the nucleation process via introducing a homo-buffer layer, this temperature can be significantly reduced by 200 degrees C. The direct-epitaxial growth ensures a good surface quality, while the temperature reduction may prevent interdiffusion in applications involving hetero multilayer structures. The films are single crystals composed of twinned domains. The constraint effect from substrate significantly limits the freedom for twinning, which leads to much less twin variants in films compared to powders. The high-quality epitaxial films obtained in this study are useful for understanding the unique phosphorescence mechanism in SA:Eu, Dy, which may further help to design new phosphor materials with higher performance.