This study investigates fluid-flow properties of the low-permeability Brentskardhaugen Bed (Knorringfjellet Formation), Wilhelmøya Subgroup, western central Spitsbergen, Svalbard. To evaluate the two-phase relative permeability of the water-CO2 system, we performed unsteady state core-flooding experiments using deionised water and gaseous CO2. The absolute permeability and residual fluid saturations were also studied. Moreover, a core plug of the Berea sandstone was tested as a reference sample. The core-flooding experiments recorded microDarcy permeability values (0.022–0.039 mD) for various differential pressures (4 to 12 MPa). The poor grain sorting and the abundance of cement were the main factors controlling the low matrix permeabilities. Closure of sub-micron fractures was the likely reason for reduced permeability with increasing effective stresses. The experimental measurements showed that CO2 fractional flow reached unity at relatively low CO2 saturation (approximately 0.35–0.45). The irreducible water saturation and trapped CO2 saturation were 56% and 23%, respectively. The corresponding endpoint CO2 and water relative permeability were 0.18 and 0.47, respectively. The results, therefore, demonstrate low endpoint CO2 saturation and low relative permeability, in addition to high CO2 fractional flow at high water saturation. The trapped CO2 saturation was relatively high, which suggests a high CO2 immobilisation capability of the Wilhelmøya Subgroup sandstones. Moreover, a lower relative permeability was observed for gaseous CO2 compared to published results for supercritical CO2. In addition, the examined core sample showed a higher trapped CO2 saturation and higher endpoint CO2 relative permeability compared with the porous and permeable Berea sandstone.