Aiming at the small output displacement of the gas-liquid temperature difference power device, a flexible hinge displacement amplification system was designed and optimized using the lever principle. The formula for calculating the magnification of the lever-type flexible hinge mechanism was derived by taking into account the offset of the flexible hinge's rotational center. Likewise, consider how the parameters of the mechanism affect the output performance of the amplifying mechanism. Combining SolidWorks and Workbench to improve the amplifying mechanism's parameters, find the best value for the parameters, and experimentally validate the optimized results. The research shows that the error between the experimental data and the finite element simulation value is 2.49%, which verifies the correctness of the simulation model. The design goals of high magnification of the mechanism and output after displacement amplification are realized.