We study volume stability of Voronoi polyhedra under hydrostatic pressures in a sodium glass. We optimize the atom positions under the pressures by an ab initio molecular dynamics method with an orbital-free density functional. The number of atoms in the supercell is 128. The change of the volumes is insensitive to pressure for the Voronoi polyhedra with smaller volumes. We introduce a method to evaluate the average charge density around individual atom. The average electron charge density around individual atom increases with decreasing Voronoi volume. The volume change of Voronoi polyhedron with signature (0,0,12,0) is the most stable to the applied pressures. The density around the atoms with the signature (0,0,12,0) is the greatest among the signatures.