In this paper, we have introduced a numerical method (SM: Shooting Method) to calculate the coupling coefficient k_p and ζ_1 of arbitrary shape gratings with any refractive index profile waveguides. Using this method, we calculate grating periods △, power reflectance R, and power transmittance T, including the influence of graded index waveguides. The results show that foe gratings with linearly graded index waveguides have the largest periods △ in order to satisfy the Bragg condition and have the largest power reflectance R.