This paper presents the design of a compact flexure-based parallel-kinematics XY precision positioning stage with constant-force output. One uniqueness of the stage is that it can produce a constant output force without using a force controller. The stage mechanism is devised using leaf flexures to achieve decoupled structures with positive stiffness. Bistable beams are used as negative-stiffness structures. By combining two negative beams and four leaf flexures, a zero-stiffness mechanism is devised. Analytical model of the zero-stiffness structure is established and verified by carrying out finite-element simulation studies. Afterwards, the structure parameters are carefully designed to cater for the requirements on the range, stiffness, resonant frequency, and payload capabilities. The parametric design is verified by conducting finite-element analysis, which reveals a sufficient reachable constant-force motion rang about 700 μm in each working axis along with better performance in other aspects.