In order to demonstrate that linearly chirped fiber gratings can be an important development direction of dispersion compensation technology, a coupling mode theoretical model of fiber gratings is introduced in this paper, and a linear chirped fiber gratings with self-constructed apodized functions is proposed for dispersion compensation. The reflection spectrum and delay characteristics of linearly chirped fiber gratings with Gaussian apodized functionsused for dispersion compensation and self-constructed apodized functions are simulated numerically. The simulation result shows that the effect of linearly chirped fiber grating with self-constructed apodized functions is better for dispersion compensation.