The objective of the work presented in this paper is to maximize the ratio of thrust to lift for a flapping NACA0012 airfoil using camber morphing. The Fish Bone Active Camber (FishBAC) is chosen as the camber morphing mechanism for this study. This mechanism can be used to improve the aerodynamic performance of an airfoil to meet the requirements of multiple flight conditions. The numerical method used for optimization is based on the method of steepest ascent. The optimization parameters include the amplitude of trailing edge deflection in morphing and its phase difference with flapping kinematics. An immersed-boundary method is used to solve the two-dimensional, unsteady, laminar flow past a flapping and morphing airfoil.