This paper presents the design of a compact flexure-based parallel-kinematics precision positioning stage with constant force output. The stage mechanism is devised using multistage compound parallelogram flexures (MCPFs) to achieve decoupled and positive-stiffness structures. Bistable beams are used to design negative-stiffness structure. Four bistable beams and six MCPFs are combined together as a zero-stiffness structure in each working direction. A complete elliptic integral model of the zero-stiffness structure is established and verified by using finite element analysis (FEA) simulation. The structure parameters are carefully designed to guarantee the requirement on motion range, stiffness, resonant frequency, and payload capabilities. The parametric design is verified by conducting FEA simulation, which reveals a reachable constant-force motion range about 700 μm in each working axis with good performance in other aspects.