A comprehensive computational fluid-dynamics-based study of a pleated wing section based on the wing of Aeshna cyanea has been performed at ultra-low Reynolds numbers corresponding to the gliding flight of these dragonflies. In addition to the pleated wing, simulations have also been carried out for its smoothed counterpart (called the 'profiled' airfoil) and a flat plate in order to better understand the aerodynamic performance of the pleated wing. The simulations employ a sharp interface Cartesian-grid-based immersed boundary method, and a detailed critical assessment of the computed results was performed giving a high measure of confidence in the fidelity of the current simulations. The simulations demonstrate that the pleated airfoil produces comparable and at times higher lift than the profiled airfoil, with a drag comparable to that of its profiled counterpart. The higher lift and moderate drag associated with the pleated airfoil lead to an aerodynamic performance that is at least equivalent to and sometimes better than the profiled airfoil. The primary cause for the reduction in the overall drag of the pleated airfoil is the negative shear drag produced by the recirculation zones which form within the pleats. The current numerical simulations therefore clearly demonstrate that the pleated wing is an ingenious design of nature, which at times surpasses the aerodynamic performance of a more conventional smooth airfoil as well as that of a flat plate. For this reason, the pleated airfoil is an excellent candidate for a fixed wing micro-aerial vehicle design.