This article presents a modified evolutionary topology optimization method for designing compliant constant force mechanisms (CFMs). CFM is defined as the mechanism that can generate constant force in the desired input displacement range, which is known as a constant force range. The force variation, i.e., fluctuation of output forces over the constant force range, is a critical parameter that reflects the stability of the output force. The key idea of the new method is that the design variables are increased or decreased for a certain small value instead of being changed between 0 (or xmin) and 1 in other evolutionary structural optimization (ESO) methods. As the CFMs have to experience a large deformation when it works, the influence of the nonlinearity needs to be considered. An additive hyperelasticity technique is utilized to alleviate the instability of the finite element analysis, which is introduced by the low-stiffness elements. The numerical examples show that the proposed design method can generate CFMs with desired constant force range and aspect ratio. The optimized CFM is manufactured by 3D printing, and the experimental result indicates that it can output an almost constant force (force variation ) in a large relative constant force range ().