Strong nonlinear behavior was observed in a LiNbO3:Fe piezoelectric resonator with a photorefractive periodic grating. The resonator is a y-cut plate with Au electrodes totally or partially deposited on both faces. The current-voltage and the admittance-frequency characteristics show nonlinear behavior such as hysteresis only near the resonance frequency. In some conditions, the current changes negatively with the voltage. These characteristics depend on the Q-value of the resonator. The present nonlinear phenomena do not occur when the Q-value is too large, while they occur at larger values of Q in usual resonators. We found that the Q-value of the resonator with the photorefractive grating varied when the resonator was annealed or when the period of the grating was changed.