A lot of flapping-wing mechanisms have been proposed to mimic the flight characteristics of biological flyers. However, it is difficult to find studies that consider the unsteady aerodynamics in the design of the flapping-wing mechanisms. This paper presents a systematic approach to optimize the design parameters of a foldable flapping-wing mechanism (FFWM) with a proper aerodynamics model. For the kinematic model, the eight design parameters are defined to determine the reference configuration of the FFWM. The geometrical constraints of each design parameter are derived, and the kinematic analysis is conducted using the plane vector analysis method. The aerodynamic simulation using an unsteady vortex lattice method is performed to compute the aerodynamic loads induced by the flapping motion. An optimization problem is formulated to search for the optimal design parameters that maximize the average lift force considering the required power corresponding to the aerodynamic torques. The parameter optimization problem is solved for three different length ratios of the outer wing to the inner wing using a genetic algorithm. The optimization results show that increasing the outer wing length can cause a significant loss in the required power. The optimal design parameters found by the proposed approach allow the FFWM to generate maximum lift force with appropriate consideration of the required power.