Graphene was grown on (0001) quartz substrate (z-cut) using catalyst free Chemical Vapor Deposition (CVD). Methane was used as a carbon source and hydrogen was introduced independently to optimize the growth. The effect of growth temperature was investigated while varying the temperature between 1000 and 1300 degrees C. With an optimized condition, a thin (< or = 2 mono-layer) continuous graphene film was grown as confirmed by Raman spectroscopy, optical transmission, and electrical measurements. The best quality film showed the Raman D-peak to G-peak intensity ratio of approximately 0.8 with the 2D-peak width of approximately 60 cm(-1). High resolution X-ray Photoelectron Spectroscopy (XPS) revealed that the grown graphene is slightly oxidized but there is no detectable Si--C chemical bond in the graphene/quartz system. Hall effect measurements exhibited a carrier mobility of approximately 400 cm2/V x s with a sheet carrier density of approximately 5 x 10(12) cm(-2).