Disclosed are an apparatus and a method of measuring porosity and permeability of a carbon dioxide underground storage medium. Both of the porosity and the permeability are measured in the state that the confining pressure is applied once. The variation characteristic in the porosity and the permeability of the core sample according to the salt precipitation occurring when supercritical carbon dioxide is injected is continuously measured. The apparatus includes a holder receiving a core sample, a pressure pump applying a confining pressure to the core sample, a gas chamber storing gas and supplying supply the stored gas to the core sample, first to third pressure gauges measuring an internal pressure of the gas chamber and front and rear portions of the holder, and a gas flow meter measuring a flow rate of gas.