The datasets contain 416 time-resolved synchrotron X-ray micro-tomographic images (grey-scale and segmented) of multiphase (brine-oil) fluid flow in a carbonate rock sample at reservoir conditions. The tomographic images were acquired at a voxel-resolution of 3.28 µm and time-resolution of 38 s. The data were collected at beamline I13 of Diamond Light Source, U.K., with an aim of investigating pore-scale processes during immiscible fluid displacement under a capillary-controlled flow regime, which lead to the trapping of a non-wetting fluid in a permeable rock. Understanding the pore-scale dynamics is important in many natural and industrial processes such as water infiltration in soils, oil recovery from reservoir rocks, geo-sequestration of supercritical CO2 to address global warming, and subsurface non-aqueous phase liquid contaminant transport. Further details of the sample preparation and fluid injection strategy can be found in Singh et al. (2017). These time-resolved tomographic images can be used for validating various 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.