Metal-organic frameworks (MOFs) as friction nanopower generation materials have attracted more and more research and attention because of the inherent three-dimensional framework structure and large aperture. In this work, the ZUT-75(Mn) with a one-dimensional pore structure was synthesized by using electron-rich benzimidazole carboxylic acid ligands, and isomorphic offspring MOF materials were obtained by single crystal-single crystal solvent-assisted metal-ion exchange. The exchange process was monitored by liquid UV-vis spectroscopy, atomic absorption spectrometry, and energy-dispersive X-ray spectroscopy. The metal-oxygen coordination energy, X-ray photoelectron spectroscopy binding energy, and hard-soft acid-base principle verified the spontaneity of the central-metal-exchange reaction. The four materials were applied to a triboelectric nanogenerator (TENG), and the output performance law of ZUT-75 was Co-MT > Zn-MT > Cu-MT > Mn-MT. Among them, the charge and power densities of Co-MT were up to 127.05 μC m-2 and 3280.50 mW m-2. When the density functional theory calculation and variable-temperature magnetic susceptibility test results were combined, it was concluded that low metal-ion-coupling degree promoted the formation and transfer of contact electrifications, which greatly improved the output performance of the TENG. This work provided a new idea for improving the output performance of the TENG.