The crystal structure of potassium sulfate, K2SO4, was studied at five temperatures from 296 down to 15 K using an off-center four-circle diffractometer. The temperature dependence of lattice constants is well explained by the Gruineisen relation. The crystal structure is confirmed to be orthorhombic, space group Pmcn, down to 15 K. The S-O bond lengths in SO4 tetrahedra with thermal motion correction are almost independent of temperature. Atomic positions of K(1), K(2) and S atoms in the beta-K2SO4 structure are found to approach the special positions in the alpha-K2SO4 structure as temperature increases. No evidence for any phase transition has been detected below room temperature.