In this paper the reflctivity peak value and bandwidth of a linearly chirped grating are calculated. A second order moment of the dispersion is defined. A quality factor is used to exactly describe the dispersion property of the grating. With this quality factor, the grating structure is optimized by selecting different coupling lengths and the distribution of coupling coefficient to improve its dispersion property. The results show that the method reported in this paper is a quantitative one being able to optimize the structure of gratings efficiently.