With the continuous development of structural seismic isolation technology, the use of seismic-isolation-device bridge designs is growing. The combination of isolation and additional damping devices is a commonly used method for controlling curved-beam bridges. Analyses of vibration control for research in the evaluation of seismic dynamic response have primarily focused on deterministic excitation, but deterministic earthquake excitation is not representative. In this study, we consider ground motion to be a uniformly modulated nonstationary random process and investigate long periods of low-frequency characteristics. Moreover, we select the Clough-Pension steady vibration power spectral model as a random vibration input for isolated curved bridges. To address the limitations of the classical optimal control algorithm, we derive vibration control equations using a sequential optimal control (SOC) algorithm. We then analyze the random responses of a curved bridge under three conditions: noncontrol, classical linear optimal control, and SOC algorithm. By establishing a curved beam bridge vibration equation of motion for random actions, we determine the displacement vibration control structure of the spectral density, acceleration spectral density response, and time variance. Analysis results show that the SOC algorithm can reduce the displacement of the isolation layer and more effectively control the seismic response of the upper structure, thus yielding a better control effect. The SOC algorithm has higher control performance and achieves better damping control.