A comprehensive investigation of the stochastic response of the approach bridge of Sutong Yangtze River Bridge-PC continuous rigid frame box girder bridges subjected to spatially varying ground motions is completed. A frame member system model considering the geometrical non-linearity caused by the dead load state and the soil-foundation-structure interaction effect is presented. The wave passage, incoherence and site-response effects are separately discussed in detail. It is pointed out that each component of the spatially varying ground motion model has important effects on the dynamic behavior of the bridge. Therefore, the variability of the ground motions should be considered in the design of this kind of bridges.