We have fabricated field-effect transistors with single-crystalline ZnO channels consisting of high-quality epitaxial films grown on lattice-matched (0001) ScAlMgO4 substrates by laser molecular-beam epitaxy. Amorphous alumina gate insulators are deposited on the top of the ZnO films using either RF magnetron sputtering or electron-beam evaporation. The field-effect mobility (mu(FE)) of the device prepared by the latter method is as high as 40cm(2.)V(-1.)s(-1), one order of magnitude higher than those typically observed for polycrystalline channel devices. However, hysteresis appears in transfer characteristics. This unfavorable effect is found to be eliminated by the thermal annealing of the entire devices in air. The much larger hysteresis and lower mu(FE) are observed for the device with sputtered gate insulators. This is presumably due to dense surface states created by ion or electron bombardment during the sputtering.