An apparatus (1) for drilling a hole in a glass plate includes recess forming means (8) for forming in a recess forming section (2) a recess (5) in an upper surface (4)of a glass plate (3) and forming therein a recess (6) communicating with the recess (5) in a lower surface (7) of the glass plate (3); chamfering means (10) for light-chamfering, in a chamfering section (9) adjacent to the recess forming section (2), edges (12, 13) of opening of each of the recesses (5, 6) in the glass plate (3) where the recesses (5, 6) have been formed by the recess forming means (8); and transporting means (11) for consecutively transporting to the recess forming section (2) the glass plates (3) in which the recesses (5, 6) are to be formed and for consecutively transporting to the chamfering section (9) the glass plates (3) in which the recesses (5, 6) have been formed.