Anisotropic stresses may induce anisotropic permeability of rocks. The present study aims at establishing the relation between permeability tensor and principal stresses for Shirahama sandstone within the pre-yield range. The effects of three principal stresses on the permeability are experimentally investigated using a Mogi-type true triaxial apparatus and transient pulse technique. Stress sensitivity coefficients of permeability are defined to describe the influence coefficients of stresses, which are found to be independent of stress states and loading paths. Based on these observations, we proposed a linear relation between the logarithm of the principal components of permeability tensor and the principal stresses.