Permeability variation is one of the key factors influencing the injectivity of CO2 in CO2 sequestration projects. Despite the research carried out on the subject, the results are highly inconsistent. In this study, the injection of brine (5 wt % NaCl + 1 wt % KCl), CO2-saturated (live) brine, and supercritical CO2 was performed on three homogeneous Berea sandstone plugs with a low clay content and two Bandera Gray sandstone plugs with a high clay content at reservoir conditions (10 MPa and 323 K). Porosity and permeability of the samples were measured using nuclear magnetic resonance (T-2 relaxation time), and a dynamic (during flooding) permeability measurement technique, respectively, at different injection rates and injection durations. The mercury intrusion test was also performed on each sample to further evaluate its pore throat size distributions. From the results of this study, it was revealed that the CO2 injection rate is unlikely to affect the permeability significantly. It was also shown that the permeability can be influenced depending upon sandstone pore throat size distribution and the distribution/structure of the clay minerals in the sample.