This paper presents the design of a new flexure-based XYZ parallel stage with near constant driving force. By combining bistable beams and positive-stiffness leaf flexures, a zero-stiffness mechanism is devised. The output motion range has been enlarged by reducing the required driving force. Analytical model of the stage is established to predict the stage performance, which is verified by conducting finite element analysis (FEA) simulation study. The structure parameters are designed to generate a reasonable performance. A prototype stage is fabricated for experimental testing. Experimental results show that the developed positioning stage delivers a constant driving force of 3.9 N within the constant-force motion range of 1 mm in each working axis.