A novel algorithm for the synthesis of fiber gratings is presented. For the first time we propose an effective optimal approach to construct a coupling coefficient function by employing 4th-order Runge-Kutta (R-K) analysis method for calculating the reflection spectra of fiber gratings. The numerical results show that with this proposed method, some required optical filters have been yielded with better features compared with other methods such as Gel’Fand-Levitan-Marchenko (GLM) algorithm. In addition, the performance of different interpolation functions particularly utilized in our algorithm, including linear-type, spline-type, and Hermit-type, are discussed in detail.