Al thin films have been grown on single-crystal MgAl2O4 spinel substrates using solid source molecular beam epitaxy. The structural properties of Al layers were systematically investigated as a function of substrate orientation. X-ray diffraction reveals that Al layers are coherently grown on both (001)- and (111)-oriented spinel substrates. However, scanning electron microscopy and atomic force microscopy show that Al layers on (001) spinel substrates display smoother surface morphology than those grown on (111) spinel substrates. Additionally, electron backscatter diffraction and transmission electron microscopy demonstrate the presence of a high density of twin domain structures in Al thin films grown on (111) spinel substrates.