Multiphase flow in permeable media is a complex pore-scale phenomenon, which is important in many natural and industrial processes. To understand the pore-scale dynamics of multiphase flow, we acquired time-series synchrotron X-ray micro-tomographic data at a voxel-resolution of 3.28 μm and time-resolution of 38 s during drainage and imbibition in a carbonate rock, under a capillary-dominated flow regime at elevated pressure. The time-series data library contains 496 tomographic images (gray-scale and segmented) for the complete drainage process, and 416 tomographic images (gray-scale and segmented) for the complete imbibition process. These datasets have been uploaded on the publicly accessible British Geological Survey repository, with the objective that the time-series information can be used by other groups to validate pore-scale displacement models such as direct simulations, pore-network and neural network models, as well as to investigate flow mechanisms related to the displacement and trapping of the non-wetting phase in the pore space. These datasets can also be used for improving segmentation algorithms for tomographic data with limited projections.