In this paper we have derived the Bragg equation of long-period fiber gratings by using interference theory. According to the color centers model and Kramers-Kronig principle, we have studied, theoretically and experimentally, the relationship between the resonant wavelength of the grating and its exposure. The result shows that the resonant wavelength of the long-period fiber grating changes with the UV exposure in the form of the sum of two decaying exponential functions an d the rate of change is controlled by the duty ratio of the mask. The resonant w avelength of the long-period fiber grating is inversely proportional to the duty ratio of the mask.