A glass plate cutting machine using a laser beam is provided to solve problems, such as uneven glass section and slanting cutting. By using the glass plate cutting machine of the current invention, the glass plate is irradiated with a first carbon dioxide laser beam of 0.05-2 joule/mm2 on a long oval shaped area of 20-200 mm2 according to an expected cutting line thereof, and immediately cooled with water, to generate a scribe line, which is then further irradiated with a second carbon dioxide laser beam of 0.1-0.5 joule/mm′ on the area of 20-200 mm2 thus obtaining a superior glass section.