Recently, flow-induced vibration and aeroelastic flutter have been considered to be an attractive energy source in renewable energy harvesting systems. However, irregular and random motions in the fluid-structure coupled dynamics greatly deteriorate the consistency and efficiency of the output power performance. Here, we report a novel mechanism of a periodic snap-through triboelectric energy harvester based on the bi-stable property of structural buckling and integrated dielectric-electrode layers made of PDMS-sealed Cu nanowire-Cu mesh. Under wind, a buckled elastic sheet experiences a periodic snap-through oscillation with a rapid transition between two opposite phases. In a regime with a large distance between two side walls, the critical free-stream velocity needed to initiate snapping increases as the wall distance becomes larger. By contrast, for a small wall-distance regime, the critical velocity decreases in an inverse manner with the wall distance. In a post-equilibrium state, three contact modes including rolling contact, head-on contact, and touch and sliding contact are identified, and their appearances strongly depend on the wall distance and free-stream velocity. The electrode layer with a small active area of 5 cm by 1 cm can deliver a maximum output power of 7.3 mW at the optimal wall distance with a free-stream velocity of 9.1 m/s. The proposed snap-through TENG system exhibits power generation performance superior to that of existing flutter-based systems, suggesting its potential applications in powering electric devices.