In the mitigation of greenhouse gas emissions, the storage efficiency and security of geological carbon storage (GCS) are the focus of attention, and both of them are closely related to the displacement behavior between immiscible two phases. In this study, CO₂-water displacement experiments were conducted on six samples with various pore structures using NMR and MRI technology to characterize the fluid distribution and determine displacement patterns. The displacement property was found to be closely related to the pore structure and appears to be independent of mineral compositions. The two-phase displacement instability gradually evolved from tounging (logCa > -2.76) to capillary fingering (logCa < -1.85), and then further evolved into viscous fingering (logCa > -1.85). Nevertheless, pore structures with good connectivity and high-permeability channels will restrain the occurrence of unstable displacement even if logCa is in the favorable range. In addition, unstable displacement is seriously affected by the heterogeneity and anisotropy of the pore structure. With the tonguing phenomenon, displacement efficiency will present a distinct ladder-shaped increase with increasing pore size, whereas the capillary fingering and viscous fingering phenomena will induce a more complex and variable change rule. Compared with unstable displacement, the stable piston-like displacement tends to result in the highest displacement efficiency. Furthermore, for rocks with high sealing efficiency that can be considered as caprocks, the pore structures are often dominated by micropores, and their displacement pattern is more likely to reflect time-consuming piston-like displacement, which will reduce the probability of premature CO₂ breakthrough.