As the electron mobility of two-dimensional (2D) materials is dependent on an insulating substrate, the nonuniform surface charge and morphology of silicon dioxide (SiO2) layers degrade the electron mobility of 2D materials. Here, we demonstrate that an atomically thin single-crystal insulating layer of silicon oxynitride (SiON) can be grown epitaxially on a SiC wafer at a wafer scale and find that the electron mobility of graphene field-effect transistors on the SiON layer is 1.5 times higher than that of graphene field-effect transistors on typical SiO2 films. Microscale and nanoscale void defects caused by heterostructure growth were eliminated for the wafer-scale growth of the single-crystal SiON layer. The single-crystal SiON layer can be grown on a SiC wafer with a single thermal process. This simple fabrication process, compatible with commercial semiconductor fabrication processes, makes the layer an excellent replacement for the SiO2/Si wafer.