The ability of dragonflies to fly in the rain without being wetted by raindrops has motivated researchers to investigate the impact behavior of a drop on the superhydrophobic wings of dragonflies. This superhydrophobic surface is used as a reference for the design of directional surfaces and has attracted extensive attention owing to its wide applicability in microfluidics, self-cleaning, and other fields. In this study, the static contact angle and rebound process of a drop impacting a dragonfly wing surface are investigated experimentally, whereas the wetting pressure, Gibbs free energy, and Stokes number vs. coefficient of restitution are theoretically calculated to examine the dynamic and unidirectional transport behaviors of the drop. Results show that the initial inclination angle of the dragonfly wing is similar to the sliding angles along with the drop sliding. The water drop bounces from the bottom of the dragonfly wing to the distal position, demonstrating directional migration. The drop impacts the dragonfly wing surface, and the drop exhibits compression, recovery, and separation phases; in these three phases, the drop morphology evolves. As the Gibbs free energy and cross-sectional area evolve, the coefficient of restitution decreases as the drop continues to bounce, and the Stokes number increases.