With the rapid development of the Artificial Intelligence technologies, means of the flow control are widely expended. However, a good understanding of the underling physics of the flow behaviours is the basis of using these technologies wisely. Inspired by the sinusoidal protrusions on pectoral flippers of the humpback whale, airfoils with a wavy leading edge tend to exhibit better aerodynamic performances and also show good potential in noise reduction. To explore the effect of the wavy leading edge on the flow over an airfoil, numerical simulations have been implemented using the delayed detached eddy simulation method at a Reynolds number of 50,000 in this paper. Aerodynamic coefficients, flow patterns and also the pressure fluctuations on the airfoil surface have been examined and discussed, which are instructive for the design of the flow measurements.