The aerodynamic effects of wing corrugation on insect flight have received widespread attention. However, there has hardly been any specific focus on dynamic changes to corrugation angle in the models. The flexible vein joints containing resilin in the wings of dragonflies and damselflies enable the longitudinal veins to rotate and thereby change the corrugation angles throughout flapping cycles. Therefore, a two-dimensional corrugated airfoil with time-varying corrugation angles is proposed and the aerodynamic performance is evaluated in terms of aerodynamic force, power and efficiency. The results indicate that the airfoil with time-varying corrugations outperforms the rigid one in terms of enhancing thrust and reducing power consumption. The aerodynamic performance of time-varying corrugated airfoils is optimal when the angle varies in a specific range, and an excessively large angle variation may have negative effects. In addition, excessive height or a negative leading edge of the corrugation can lead to a reduction in the thrust. A design concept for the 2D airfoil with time-varying corrugations is provided and the findings are of significance for enhancing the aerodynamic performance of biomimetic flexible flapping-wing vehicles.