To overcome the problems of gas release, energy waste and pipeline leakage of dust erosion wear caused by the fluctuation of the by-product gas pressure in iron and steel enterprises, a 3D mathematical model of a by-product gas pipeline network was constructed in this study. Multi-condition numerical simulation analysis and spatiotemporal pressure fluctuation prediction modelling were also conducted. Firstly, the 3D mathematical model of a by-product gas pipeline network, with an error < 10%, was established by using computational fluid dynamics. Secondly, numerical simulations were conducted under multiple working conditions to study the pressure fluctuation law of the pipeline network and the erosion wear of the pipe wall. Finally, a rapid, accurate, adaptable prediction model was constructed using a spatiotemporal graph convolutional gated recurrent unit method with a combination of the numerical simulation data and pressure fluctuation law. The pressure fluctuation of the by-product gas pipeline network after a change in the blast furnace flow could be predicted in <2 s and the mean absolute percentage error of the prediction was < 2.6%.