The fact that single-layer graphene can be visualized on 300 nm SiO(2)/Si substrate using an optical microscope has enabled the facile fabrication of single-layer graphene devices for fundamental studies and potential applications. Here we report on an Al(2)O(3)/Si substrate for the fabrication of graphene devices with better contrast and higher performance. Our studies show that the contrast of single-layer graphene on 72 nm Al(2)O(3)/Si substrate is much better than that of single-layer graphene on 300 nm SiO(2)/Si substrate. Moreover, the transconductance of single-layer graphene transistors on Al(2)O(3)/Si substrate shows a more than sevenfold increase, due to the smaller dielectric thickness and higher dielectric constant in a 72 nm Al(2)O(3) film. These studies demonstrate a new and superior substrate for the fabrication of graphene transistors, and are of significance for both fundamental studies and technological applications.