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In order to solve the geometric nonlinear problem of the positive stiffness module in the compliant constant-force mechanism, the positive stiffness module was designed based on the semicircular corrugated periodic beam, the negative stiffness module adopted a bistable beam, and the compliant constant force mechanism was designed by using the principle of positive and negative stiffness superposition. The theoretical model of the positive stiffness module was established by using the Mohr integral method and the compliance matrix method, and the theoretical model of the negative stiffness module was established by the elliptic integral method. The force-displacement curve of the compliant constant force mechanism was analyzed by ANSYS finite element simulation software to verify the theoretical model, and the relative error between the two was within 10%. In order to expand the range of constant-force, the response surface method was used to optimize the geometric parameters of the compliant constant-force mechanism, and the sensitivity analysis of the geometric parameters affecting the constant-force range was carried out. The prototype of the compliant constant-force mechanism was processed by 3D printing technology for experimental verification. The experimental results showed that the mechanism can maintain a constant-force of about 18.8N within the input displacement range of 1.1~6.2mm. The feasibility of the designed compliant constant-force mechanism, the validity of the optimization method and the accuracy of the theoretical model were verified.