Insulating AlN single crystals were grown on 6H-SiC substrates by molecular beam epitaxy (MBE). The insulating properties of AlN were investigated by a current-voltage (I-V) measurement of Al/AlN/6H-SiC metal-insulator-semiconductor (MIS) diode structures. 6H-SiC substrates pretreated by HCl gas etching had no surface polishing scratches and an atomically flat surface. The AlN layer grown on the atomically flat substrate was very smooth and exhibited excellent insulating properties. The resistivity of this layer was around 7x10(13) Omega cm. Thinner AlN layers had superior insulating properties. From the result of X-ray diffraction (XRD) measurements, thinner AlN layers had superior structural quality. These results indicate strong correlations between insulating properties and structural quality of AlN layer.