Carbon capture and storage (CCS) is an essential technology for achieving carbon neutrality. Depositional environments with sandstone and interbedded shale layers are promising for CO2 storage because they can retain CO2 beneath continuous and discontinuous shale layers. However, conventional numerical simulation of shale–sandstone systems is computationally challenging due to the large contrast in properties between the shale and sandstone layers and significant impact of thin shale layers on CO2 migration. Extending recent advancements in Fourier neural operators (FNOs), we propose a new deep learning architecture, the RU-FNO, to predict CO2 migration in complex shale–sandstone reservoirs under various reservoir conditions, injection designs, and rock properties. The gas saturation plume and pressure buildup predictions of the RU-FNO model are 8000-times faster than traditional numerical models and exhibit remarkable accuracy. We utilize the model’s fast prediction to investigate the impact of shale layer characteristics on plume migration and pressure buildup. These case studies show that shale–sandstone reservoirs with moderate heterogeneity and spatial continuity can minimize the plume footprint and maximize storage efficiency.