In general, a conventional flap on an aircraft wing can reduce the aerodynamic efficiency due to geometric discontinuity. On the other hand, the aerodynamic performance can be improved by using a shape-morphing wing instead of a separate flap. In this research, a new flap morphing mechanism that can change the wing shape smoothly was devised to prevent aerodynamic losses. Moreover, a prototype wing was fabricated to demonstrate the morphing mechanism. A shape memory alloy (SMA) wire actuator was used for the morphing wing. The specific current range was measured to control the SMA actuator. The deflection angles at the trailing edge were also measured while various currents were applied to the SMA actuator. The trailing edge of the wing changed smoothly when the current was applied. Moreover, the deflection angle also increased as the current increased. The maximum frequency level was around 0.1 Hz. The aerodynamic performance of the deformed airfoil by the SMA wire was analyzed by using the commercial program GAMBIT and FLUENT. The results were compared with the results of an undeformed wing. It was demonstrated that the morphing mechanism changes the wing shape smoothly without the extension of the wing skin.