Based on a single long period fiber grating (LPFG) with optical fiber pigtail coated with highreflective film, a LPFG Michelson interferometer with partly etched fiber cladding LPFG is designed. It improves the LPFG sensitivity. By applying interference principle, the change of interference peaks along with environment refractive index is obtained. The refractive index sensitivity of no etched LPFG Michelson interferometer is compared with that of the etched LPFG Michelson interferometer, results show that the change of the refractive index sensitivity is significantly improved. The peak wavelength of interferometer shifts from 0.9 nm to 3.4 nm when liquid refractive index is 1.333 and 1.352.