To ensure sequestration safety, confirming the injectivity of the reservoir rock formation is of critical importance, requiring studies of the rock permeability to uncover the fluid migration scenarios within the porous reservoir rock. Two-phase (super-critical CO₂-brine) flow behavior following the post CO₂ injection is believed to be a dominating factor; its flooding behavior within the porous rock media needs to be further clarified prior to confirming the feasibility of domestic CO₂ geo-sequestration. This study aims to determine the relative permeability of rock cores obtained from field outcropping. A test facility was established to determine the relative permeability during drainage and imbibition processes using a core-flooding test characterized by displacement method. The test facility was assembled locally and is regarded as a pioneering attempt. By relevant data interpretation, the parameters of relative permeability for predicting the movement of super-critical CO₂ after injection can be modeled. More reliable parameters can be obtained using history matching processes wherein time-elapsed data calibration is used in conjunction with a computer code, TOUGH2. The test results were iteratively calibrated using numerical simulation by conducting a history matching process. The K-S curves derived from best-fit parameters are believed to be the most relevant relative permeability for the reservoir rock. Through this preliminary study, a better understanding of some of the problems and limitations associated with the determination of the rock relative permeability using two-phase flow test is achieved, but more advanced research is required.