Ultra-precision positioning systems basically require high natural frequency and sufficient workspace. To cope with this requirement, flexure hinge mechanisms have been proposed. However, previous designs have difficulty satisfying the functional requirements of the system due to problems in the modeling and optimization process since they are coupled. Therefore, this paper performs optimum design of a planar 3-D ultra-precision positioning mechanism using a booster based on axiomatic design. Based on preliminary kinematic analysis and dynamic modeling of the system, an optimum design is conducted. To examine the effectiveness of the optimal parameters obtained by a theoretical approach, a simulation is performed by FEM. The simulation result shows that a natural frequency of 200.53Hz and a workspace of 200 μm x 200 μm can be ensured, which is in very close agreement with the specified goal of design.