Abstract: Numerical methods for solving a set of nonlinear coupled equations of fiber Bragg grating (FBG) were reviewed. Characteristics of prediction-correction system based on implicit Runge-Kutta method were analyzied.To achieve simple, efficient and high precision numerical simulation for nonlinear coupled mode equations of fiber Bragg grating, we designed a prediction-correction system based on continued fraction correction method, and compared it with other methods. The segment length of grating can be greatly increased to save computing time through this method ,and the convergence of calculation always exists. The comparison of errors shows that the simulation method is accurate. By this method, uniform numerical simulation model is established under static and dynamic circumstances based on physical process of optical wave transmission in grating. Many skills in simulation are researched. Nonlinear transmission characteristics of FBG were studied numerically when continuous wave (CW) and pulse were input.