This paper investigates an unconventional honeycomb cellular structure featuring a negative Poisson’s ratio with the ability to undergo large overall displacements with limited straining of its solid material in the spanwise direction. Numerical analyses are performed to exploit such properties in the design of a morphing airfoil. The commercial simulation software ANSYS is used to carry on these processes. The cellular structure is designed to satisfy the requirements of configuration changing occurred while wing morphing. Finally, detailed numerical models of the structures are presented as a possible approach to evaluate the stress distribution of the structure. According to simulation results, the airfoil designed in this paper has the property of negative Poisson’s ratio, which is useful to the morphing wing aircraft design.