We explain the molecular mechanism of the effect of urea and glycerol cosolvents on the partial molar volume (PMV) change associated with the pressure denaturation of staphylococcal nuclease (SNase) protein recently observed in experiments. Native and denatured conformations of SNase are produced by using molecular dynamics simulations in water, and the PMV is obtained from the integral equation theory of molecular liquids called 3D-RISM, which is based on statistical mechanics. The PMV of the native SNase in water predicted by 3D-RISM theory is in good agreement with experiment. The PMV changes associated with pressure denaturation in water and in water-urea and water-glycerol mixtures are qualitatively reproduced. By analyzing the results obtained, we found two interesting cosolvent effects on the PMV: (1) both urea and glycerol cosolvents increase the PMVs of both native and denatured SNase compared to those in water and (2) both urea and glycerol cosolvents increase the PMV of denatured SNase more than that of native SNase. We also showed that these two observations can be explained in terms of the thermal volume, which is related to the packing effect of solvent molecules.