This paper presents an optimal aerodynamic morphing wing based on the compliant mechanisms. Taking a particular type of UAV (Unmanned Aerial Vehicle) wing as the research object, the continuous deflection deformation of the leading and trailing edge under the high efficiency is analyzed, the parametric design requirements of the variable curvature are put forward. The least square error (LSE) between the deformed and target displacement of the control points is defined as the objective function. After that, the optimization model of the compliant mechanism is established based on the solid isotropic material with penalization (SIMP) model. Through the topology optimization design of compliant mechanisms, the leading and trailing edges of the morphing wing can be continuously smooth deflected. The aerodynamic characteristics of the optimization results under the deformation state are calculated and analyzed, and the influence of the leading and trailing edge deformation on the aerodynamic characteristics is tested, which demonstrate the effectiveness of the proposed method.