Anti-reflection coating films have used to increase the transmittance of displays and enhance the efficiency of solar cells. Hydrophobic anti-reflection coating films were fabricated on a glass substrate by sol-gel method. To fabricate an anti-reflection film with a high transmittance, poly ethylene glycol (PEG) was added to tetraethyl orthosilicate (TEOS) solution. The content of PEG was changed from 1 to 4 wt% in order to control the morphology, thickness, and refractive index of the $SiO_2$ thin films. The reflectance and transmittance of both sides of the coated thin film fabricated with PEG 4 wt% solution were 0.3% and 99.4% at 500 nm wavelength. The refractive index and thickness of the thin film were n = 1.29 and d = 105 nm. Fluoro alkyl silane (FAS) was used for hydrophobic treatment on the surface of the anti-reflection thin film. The contact angle was increased from $13.2^{circ}$ to $113.7^{circ}$ after hydrophobic treatment.