The temperature-independent fiber Bragg grating (FBG) displacement measurement based on optical reflection spectrum bandwidth modulation and differential optical power detection is proposed and experimentally demonstrated. A specially designed bending cantilever beam is used to induce Gauss strain distribution along the sensing FBG, resulting in Bragg wavelength shift and bandwidth modulation. Based on the theory of optical waveguide and material mechanics, the causation of reflection spectrum lateral gradient broadening of fiber Bragg grating under the Gauss strain distribution is analyzed, and the force-to-bandwidth broadening relation and force-to-optical power relation are formulized based on cantilever beam special structure with a lateral gradient broadening of FBG spectrum bandwidth and a linear increase of reflection optical power. For a temperature range of -10 ℃～80 ℃, the measured displacement fluctuates less than 1.2% without any temperature compensation.