Long-period fiber grating is a new kind of fiber device developed in recent years, which couples light from the forward-propagating guided core mode into co-propagating cladding modes at special wavelengths, with more advantages over normal fiber gratings at the aspects of temperature，strain，refractive index sensing. Based on coupled mode theory, the resonant wavelength of LPFG was discussed and its transmission spectrum was simulated. The sensitivity of the long-period gratings to the surrounding refractive index was analyzed theoretically, and the relationship between the surrounding refractive index factors and the cladding mode orders was discussed while the sensitivities at different surrounding refractive index were compared. The changing rule of the resonant wavelength versus the surrounding refractive index was simulated, under the condition of the surrounding refractive index less than the cladding refractive index.