To overcome the constraint of conventional tilted beam-based bistable mechanism, this paper proposes a novel type of bistable structure based on tilted-angle compound parallelogram flexure to achieve a larger stroke of negative stiffness region while maintaining a compact physical size. As an application of the presented bistable mechanism, a flexure constant-force micropositioning stage is designed to deliver a large stroke. The constant force output is obtained by combining a bistable flexure mechanism with a positive-stiffness flexure mechanism. To facilitate the parametric design of the flexure mechanism, analytical models are derived to quantify the stage performance. The models are verified by carrying out nonlinear finite-element analysis (FEA). A metal prototype is fabricated for experimental study. Results demonstrate the effectiveness of the proposed ideas for a long-stroke, constant-force compliant mechanism dedicated to precision micropositioning applications. Experimental results also show the appearance of two-stage constant force due to the manufacturing errors of the bistable beams.