A Michelson interferometer based on fiber ring and a LPFG is presented.The input signal is partly coupled into the cladding of the fiber by LPFG,both of the transmitted optical signals in the core and cladding are reflected by sagnac fiber ring and coupled simultaneously back to the LPFG and interfere.Spectrum characteristics are analyzed using transfer matrix method.The proposed device is experimented to serve a sucrose concentration sensor,whose sensitivity is measured to be 0.065 nmLg-1.