A novel airfoil noise reduction technique, based on morphing structures, has been introduced and investigated. In order to achieve high aerodynamic performance and reduce the noise, a new morphing flap concept based on a bending stiffness tailored honeycomb core with zero Poisson's ratio has been developed. The response of the morphing structure to an internal actuation force is investigated using a two-dimensional finite element model. In this study, a NACA 63-418 airfoil of chord 1.3m has been fitted with the morphing flap. The aerodynamic and acoustic performance of the airfoil is studied using Xfoil and the BPM semi-empirical airfoil noise prediction model. A parametric study is provided for the effects of the changes to the profile and curvature of the pressure and suction sides of the airfoil trailing edge. The effectiveness of the proposed method is investigated at different Mach numbers and angles of attack. Results have shown that both the aerodynamic and acoustic performance of the airfoil will significantly improve as a result of the morphing trailing edge. Also, the preliminary optimization of the morphing flap design has shown that by changing the bending stiffness of the honeycomb core along the chord, the morphing profile can be tailored, leading to aerodynamic performance improvement and significant noise reduction at low frequencies.