The seepage property of low-permeability rock is of significant importance for the design and safety analysis of underground cavities. By using a self-developed test system, both permeability and porosity of granite from an underground oil storage depot were measured. In order to study the influence of rock types on permeability, a tight sandstone was selected as a contrast. The experimental results suggested that the porosity of this granite is less than 5% and permeability is low to 10–20 m2 within the range of effective stress. During the loading process, both exponential relationship and power law can be utilized to describe the relationship between effective stress and permeability. However, power law matches the experimental data better during the unloading condition. The stress dependent porosity of granite during loading process can be described via an exponential relationship while the match between the model and experimental data can be improved by a power law in unloading paths. The correlation of permeability and porosity can be described in a power law form. Besides, granite shows great different evolution rules in permeability and porosity from sandstone. It is inferred that this difference can be attributed to the preparing of samples and different movements of microstructures subjected to effective stress.