This paper reports for the first time the successful growth of a single GaN layer on an amorphous glass substrate using metal organic chemical vapor deposition (MOCVD) technique. The layers were characterized by room temperature photoluminescence and X-ray diffraction measurements. In addition, the lateral overgrowth of GaN on this substrate was also tried, which could provide an effective method to obtain high-quality GaN substrates in the near future. In comparison to the overgrowth on sapphire substrate, the lateral overgrowth on our substrate is independent of the mask stripe direction, which could indicate a different growth mechanism.