In order to innovate the wind energy harvesting method based on galloping and improve galloping-based triboelectric nanogenerator wind energy harvesting performance, a galloping-based square cylinder triboelectric nanogenerator (GSC-TENG) is proposed in this work. The GSC-TENG consists of a square cylinder bluff body, a triboelectrification embedded in the bluff body, a cantilever beam and a base. The response of the aerodynamics and power generation performance of the GSC-TENG with a high mass ratio (m*=526.6) to the system damping ratio (0.0106, 0.0304 and 0.0568) and wind speed (0.6–12.4 m/s) are studied through CFD simulation and wind tunnel test. The critical wind speed, amplitude and power generation performance of systems with different damping ratios are analyzed in detail, and the wind speed range corresponding to the maximum amplitude is determined. By increasing the stiffness and damping ratio of the system, the output performance under high wind speed conditions can be enhanced and stabilized. Compared with the GSC-TENG with damping ratio 0.0106, the output power of the GSC-TENG with damping ratio 0.0568 at the wind speed of 4.0 m/s is enhanced by 141 times, which is up to 62.25 W/m3. To harness a broadband wind energy, a novel galloping-based TENG is introduced. Analyzing the dynamic characteristics of square cylinder bluff body with different damping ratios is of significant meaning to the design and improve of the galloping-based triboelectric wind energy harvester.