A glass-plate working apparatus comprising: a scribe line forming device for forming scribe lines on two glass plates; a glass-plate bend-breaking device (15A, 15B) for bend-breaking the two glass plates; a first glass-plate peripheral edge grinding device adapted to grind peripheral edge of one of the two glass plates; a second glass-plate peripheral edge grinding device adapted to grind peripheral edge of another one of the two glass plates; and a glass-plate transporting device for carrying in and carrying out the two glass plates at a time with respect to each of the scribe line forming device, the glass-plate bend-breaking device (15A, 15B), the first glass-plate peripheral edge grinding device, and the second glass-plate peripheral edge grinding device characterized in that, said first glass-plate peripheral edge grinding device has a first grinding worktable to suck and support the one glass plate and move along a Y-axis in a direction Y, a first Y-axis moving means for moving the first grinding worktable along the Y-axis, a first grinding head to move along a X-axis in a direction X, and a first X-axis moving means for moving the first grinding head along the X-axis, said second glass-plate peripheral edge grinding device has a second grinding worktable to suck and support the other glass plate and move along the Y-axis in the direction Y, a second Y-axis moving means for moving the second grinding worktable along the Y-axis, a second grinding head to move along the X-axis in the direction X, and a second X-axis moving means for moving the second grinding head along the X-axis, said first grinding worktable and the second grinding worktable are adapted to be moved along the Y-axis mutually independently by the first Y-axis moving means and the second Y-axis moving means, said first grinding head and the second grinding head are adapted to be moved along the X-axis mutually independently by the first X-axis moving means and the second first X-axis moving means, X-Y coordinate system controlled movement of the first and second glass-plate peripheral edge grinding devices (19A, 19B) being adapted to be effected independently of each other. a scribe line forming device for forming scribe lines on two glass plates; a glass-plate bend-breaking device (15A, 15B) for bend-breaking the two glass plates; a first glass-plate peripheral edge grinding device adapted to grind peripheral edge of one of the two glass plates; a second glass-plate peripheral edge grinding device adapted to grind peripheral edge of another one of the two glass plates; and a glass-plate transporting device for carrying in and carrying out the two glass plates at a time with respect to each of the scribe line forming device, the glass-plate bend-breaking device (15A, 15B), the first glass-plate peripheral edge grinding device, and the second glass-plate peripheral edge grinding device characterized in that, said first glass-plate peripheral edge grinding device has a first grinding worktable to suck and support the one glass plate and move along a Y-axis in a direction Y, a first Y-axis moving means for moving the first grinding worktable along the Y-axis, a first grinding head to move along a X-axis in a direction X, and a first X-axis moving means for moving the first grinding head along the X-axis, said second glass-plate peripheral edge grinding device has a second grinding worktable to suck and support the other glass plate and move along the Y-axis in the direction Y, a second Y-axis moving means for moving the second grinding worktable along the Y-axis, a second grinding head to move along the X-axis in the direction X, and a second X-axis moving means for moving the second grinding head along the X-axis, said first grinding worktable and the second grinding worktable are adapted to be moved along the Y-axis mutually independently by the first Y-axis moving means and the second Y-axis moving means, said first grinding head and the second grinding head are adapted to be moved along the X-axis mutually independently by the first X-axis moving means and the second first X-axis moving means, X-Y coordinate system controlled movement of the first and second glass-plate peripheral edge grinding devices (19A, 19B) being adapted to be effected independently of each other.