We investigate influence of the electron-phonon interaction on persistent current in a mesoscopic ring threaded by a Aharonov-Bohm flux Φ. We find that all thermodynamic quantities are still periodic in Φ with a period Φo = hc/e. In both cases, weak- and strong-coupling, effective mass of the electrons is increased and amplitude of persistent current is suppressed. In the latter case the amplitude decreases exponentially as a function of the electron-phonon coupling constant.