This paper presents the design of a flexure-based precision positioning micro-motion stage system with constant output force. The stage mechanism is devised using folded leaf flexure (FLF) to achieve positive-stiffness structure. Bistable beams are employed to design negative-stiffness structure by using their buckling characteristics. Two bistable beams and two FLFs are combined together as a zero-stiffness structure. Complete models of the amplifier and the zero-stiffness structure are established and verified by using finite element analysis (FEA) simulation. The structural parameters are carefully designed to guarantee the performance requirement of motion range, stiffness and driving force. A prototype stage is fabricated by 3D printing process and a series of experiments are conducted for performance testing. Experimental results show that the developed positioning stage delivers a reachable constant-force motion range of 138 μm with good motion repeatability.