The conditions of depositing graded refractive index silicon oxy-nitride films were studied when the optical properties of the films changed with the composition. SiOxNy thin films of different N/O ratios were deposited by rf magnetron reactive sputtering. Samples' refractive index, extinction coefficient, composition and deposition rate were studied. The transmission curve was measured by using UV-VIS spectrophotometer. A simple and accurate method is presented for determination of the optical constants and physical thickness of thin films. Which consists in fitting the experimental transmission curve with the help of the physical model. The composition of SiOxNy films was analyzed by X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spoctroscopy (FTIR) characterization methods. The experiments indicated the film characteristics were related closely to the N2/O2 gas flow ratio. As a result, the samples' refractive index can be controlled from 1.92 to 1.46 by adjusting the gas flow and controlling the total pressure, and the optical gap calculated using Wemple-DiDomenico single-oscillator model lies between 5～6.5 eV.