To ensure the safe geological disposal of radioactive waste, it is important to determine the permeability (hydraulic conductivity) of clays. The transient pulse method is suitable for low-permeability materials because it requires a relatively short time to determine their permeability. Upstream pore pressure typically increases in the measurement conducted via the transient pulse method. However, this procedure cannot be used to determine the permeability of clays due to the increase in pore pressure. Therefore, the transient pulse method has never been applied to determine clay permeability. In this study, we applied the transient pulse method to a clay sample obtained in the Mizunami Underground Research Laboratory to determine its permeability while decreasing the downstream pore pressure. We found that this method was also appropriate for conducting measurements on granite. The hydraulic conductivity of the clay measured by the proposed method was higher by only one order of magnitude than that determined using the falling head method, indicating that hydraulic conductivity can be determined using the transient pulse method with reasonably small error. The measurement time of the transient pulse method was much shorter than that of the falling head method. We concluded that the transient pulse method is appropriate for determining clay permeability.