To explore the coupling mechanism of the time-varying fluid-solid coupling vibration of the medium flowing through the pipeline on the seismic response, the oil pipeline supported on the diagonal spanning structure is taken as the research object. Considering the time-varying characteristics of the dynamics during the medium flowing process through the pipeline and adopting the two-way fluid-solid coupling theoretical model, the theoretical method for calculating the coupling between the medium time-varying fluid-solid coupling vibration and seismic response is proposed, and a finite element simulation model for the coupled medium-pipeline-span system is established. By setting the calculation parameters and boundary conditions of the coupling interface, the simulation is carried out. In the finite element simulation model, by setting the calculation parameters of the medium, fluid, pipeline, crossing structures, and considering the boundary conditions of the coupling interface, simulation calculations were carried out. The displacements and acceleration responses at the end of the bridge platform and the cross-section of the pipeline across the location were extracted for calculations and comparative analysis with the calculation results without considering the medium flowing vibration effects was carried out. The results show that: when the medium flows from the left side of the pipeline to the right side over time, the state changes of different fluids in the pipeline caused by the medium flow and the seismic coupling result in differences in the pipeline displacement response and acceleration response distributions along the pipeline length. When the source of the medium flow reaches about 4/5 of the pipeline length over time, the peak displacement response and peak acceleration response of the media occur all the time. The coupling response of the right half of the pipeline is larger than that of the left half of the pipeline, and the calculation results of the pipe cross-section at six typical locations in the right half of the cross-section reveal the general rules of the medium flowing vibration coupling with the seismic response. Under the same conditions, the displacement coupling response of the pipeline considering the medium flowing vibration effects coupling with seismic response is approximately 2.7 times that without considering the medium flowing vibration effects. It indicates that the fluid-solid coupling vibration considering the medium flowing vibration effects has non-negligible effects on the earthquake response.