Based on coupled-mode theory, the eigen equations of core and cladding modes of the three-layer dielectric long-period fiber grating (LPFG) are presented by using strict mathematical model. Changes of effective indexes of the core and cladding modes in LPFG with refractive index of external environment are described, and the influence of the changes of the refractive index of external medium on resonant wavelength of LPFG is analyzed. The sensitivity of sensing measurement of LPFG can be significantly improved by coating with a specific film whose refractive index is sensitive to the change of the external environment, which provides a theoretical support to the optimum design of LPFG sensor and its practical application.