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We investigate magnetic-flux-induced persistent currents (PCs) in a one-dimensional nonlinear mesoscopic ring based on the Frenkel–Kontorova (FK) model. By applying a transfer-matrix technique, the energy spectra, the PCs, and the Thouless exponent are theoretically obtained. It is shown that the energy spectrum splits into sub-bands when the on-site energy is gradually increased, and in the flux-dependent energy spectra, the energy levels show different behaviors over the transition by breaking of analyticity. Meanwhile, the PC is determined by the magnetic flux, the on-site energy, and the Fermi level. The increment of the on-site energy leads to a dramatic suppression of the PC. When the Fermi level is in the vicinity of “band” gaps, the PC is limited considerably; otherwise, the PC increases by several orders of magnitude. The suppressed PC is related to the electronic localization of the FK ring, which is described by the Thouless exponents. Our investigations provide detailed information about the influence of nonlinear structure on the PC and contribute to its potential application in quantum devices.