A compliant constant-force mechanism is a soft and passive force regulation mechanism that can provide a nearly constant output force over a range of input displacements. This study presents a topology and geometry optimization procedure to design a fully compliant constant-force mechanism. A topology optimization method is used to synthesize the optimal layout of a compliant constant-force mechanism from an initial design domain with pre-specified boundary conditions, and a geometry optimization method is further used to identify detailed geometric parameters for the design. The optimized compliant constant-force mechanism is prototyped by 3D printing using thermoplastic elastomer. Experimental results show that the proposed design can generate a nearly constant output force at output port within the desired input displacement range. The presented design is expected to be used for various applications in the emerging fields such as soft robots and flexible mechatronics.