Steel–concrete composite box girder (SCC BG) is widely used in engineering because it can make full use of the tensile properties of steel and the compressive properties of concrete. However, research on the vibrational transmission and vibroacoustic response of the SCC BG is still relatively rare. In this study, a laboratory hammering test was performed to obtain the dynamic characteristics of a scaled specimen of an SCC BG before and after installing a concrete deck. The experimental results revealed that the vibroacoustic response was greatly reduced after the installation of concrete deck due to a reduction in the transmission of on-deck vibrations to the steel box girder. Following this, we introduce a model to predict the structural vibroacoustic response of the SCC BG based on the hybrid finite element–boundary element–statistical energy analysis method, and verify its accuracy through experiments. The accurately calibrated model is then used to study the characteristics of vibration transmission between plates of the SCC BG. The influences of the thickness of the concrete deck, concrete material, and degree of shear connection on vibroacoustic responses of the SCC BG are also discussed.