The isolated curved beam bridge will produce large elastic-plastic deformation under strong earthquakes, thus certain control measures need to be taken to ensure its safety. The classical Bouc-Wen model was used to establish the nonlinear dynamic equation of isolated curved beamSbridge considering upper structure’s eccentricity, and the dynamic response of the structure under the action of rare earthquake was solved. In view of the large elastic-plastic deformation caused by strong earthquakes, the nonlinear vibration control equation of isolated curved beam bridge was established. And after equivalent linearizing of the equation, sequential optimal control algorithm (SOC) and classical linear optimal control (COC) were used to to study the vibration control of the bridge. The results show that when the isolated curved beam bridge was subjected under rare earthquakes, the lower structure and the isolation layer of the curved bridge have entered the plastic stage and a small amount of residual displacement has been generated. Both the sequential optimal control algorithm and classical linear optimal control can effectively reduce the horizontal displacement and residual displacement of the isolated curved beam bridge in the elastic-plastic condition, and effectively restrain the torsional effect of it, among which the sequential optimal control algorithm can significantly reduce the peak response of the curved bridge compared with the classical optimal control algorithm.