A method and an apparatus for tempering glass sheets. A glass sheet is heated to a tempering temperature and quenching is conducted by blasting cooling air to both surfaces of the glass sheet. The quenching of a top surface and a bottom surface of the glass sheet's both side portions is commenced earlier or is performed at the early stage of quenching more effectively than the quenching of a top surface and a bottom surface of the glass sheet's intermediate portion. As a result, the compression stress required for a desired tempering degree is established on both surfaces of the side portions earlier than on both surfaces of the intermediate portion. In order to achieve this, the cooling air enclosures above and below a glass sheet are provided with a subarea of weakened cooling effect.