Hybrid vibration control, involving the combined use of feedforward and feedback control, is developed for a cable-stayed bridge using passivity-based control. The control objective is to reject all disturbances that cause unwanted motion in the bridge structure, namely seismic activity, wave loading and wind loading, while keeping energy consumption at a very low level. An experimental bridge prototype has been developed and simulations involving an analytical model derived from real data are presented. A three dimensional finite element model was developed of the bridge for verification purposes. A multiple time step ahead estimator is also developed using neural networks that is used in the feedforward loop to predict future bridge motion using past values of disturbance and output. Simulation results of the neural estimator are presented.