A theory analysis of fiber grating soliton was implemented using the matrix transfer function based on the principle of electromagnetic field and electromagnetic wave. The electromagnetic model of light wave of fiber grating soliton was established and described by the vector expression with complex amplitude. The Cayley-Hamilton theorem and Chebychev polynomial of the second kind were used to compute and prove the model. The reflectivity and transmissivity based on the matrix transfer function were emulated to get the analysis on characteristics of fiber long(short)-period grating and deep(light)- modulation grating, and the difference between the forward wave propagation and the backward wave propagation on initial grating has an impact on the electromagnetic wave of grating soliton on terminal grating. It is a common value to analyze the characteristic of nonlinear fiber grating and the diversified fabrication of fiber grating.