A glass-plate working machine 1 is arranged such that while a cutting head 9 for forming a cut line on a glass plate 5 and a grinding head 10 for grinding a peripheral edge of the glass plate 5 bend-broken along the cut line are being moved simultaneously in parallel under numerical control, the cutting head 9 and the grinding head 10 respectively having angle control motors 46 and 49 are synchronously subjected to angular control about axes 39 perpendicular to the surface of the glass plate 5, and the cutting head 9 and the grinding head 10 are moved such that the orientation of a cutter wheel 52 is adjusted to a processing line, and the press contacting direction of a grinding wheel 64 of the grinding head 10 is kept in a normal direction with respect to a processing line of an edge of the glass plate 5.