In this paper, a new scheme to measure the difference of two resonance wavelengths of a fiber Bragg grating (FBG) load sensor is presented. In order to acquire high primary resolution of the fiber grating transverse load sensing, a beam splitter and a Michelson interferometer with two Faraday rotation mirrors (FRM) are adopted to compose the detecting system, the instability caused by birefringence of the fibers in the interferometer is considerably reduced. This new FBG load senor is demonstrated and the primary resolution of 0.025 N/mm is obtained.