ZnO films with MgO buffer layers were grown on (0001) Al2O3 by using plasma-assisted molecular beam epitaxy (PAMBE). We investigated the effect of the MgO buffer thickness on the growth of the ZnO films on (0001) Al2O3 by using PAMBE with neither intentional annealing of the MgO buffer nor low-temperature ZnO growth. The MgO buffer thickness strongly affected the crystal quality of the ZnO films. We believe that the crystal quality of the MgO buffer itself would be the most important factor affecting the crystal quality of the ZnO film on it.