A Michelson interferometer based on a single long-period fiber grating (LPFG) is presented. The input signal is partly coupled into the cladding of the fiber by LPFG, and the pigtail of the LPFG is coated with high reflection film (RF). Therefore, both of the transmitted optical signals in the core and cladding are coupled simultaneously back to the LPFG and interfere by the HR coating. The interference characteristics are analyzed theoretically. The fringe-shift of the interference spectrum shows good linear relationship to the temperature, which is measured to be 31.3 pm/℃ in the experiment. The proposed device is expected to serve a high temperature sensor, as well as WDM filter.