A glass-plate working apparatus comprising a grinding head, which is adapted to move in an X-axis direction which is the transporting direction of the glass plate, characterized by comprising: two grinding worktables (17A, 17B) which undergo NC controlled movement or angularly controlled rotation independently of each other; and wherein the grinding head undergoes NC controlled movement in correspondence with the two grinding worktables (17A, 17B), wherein the two grinding worktables (17A, 17B) alternately move in a planar coordinate system in cooperation with the grinding head and alternately repeat operation in which while one of the grinding worktables, while holding a bend-broken glass plate, is effecting grinding of peripheral edges of the bend-broken glass plate by the grinding head, another one of the grinding worktables effects an operation of discharging a ground glass plate and receiving a next glass plate, to thereby allow the grinding head to effect grinding of consecutively received glass plates on a continual basis, wherein either: (a) said two grinding worktables (17A, 17B) move independently of each other in a Y-axis direction perpendicular to a direction of transporting the glass plate and are arranged in the transporting direction of the glass plate; and wherein said grinding head is adapted to move in an X-Y planar coordinate system in a changing manner with the grinding worktable holding the glass plate and effect grinding on a continual basis; or (b) said two grinding worktables (17A, 17B) are adapted to undergo angularly controlled rotation independently of each other and move in a Y-axis direction perpendicular to a transporting direction of the glass plate; and said grinding head is adapted to move in a planar coordinate system alternately in cooperation with each of the two grinding worktables (17A, 17B), the two grinding worktables being arranged in series in the transporting direction of the glass plate. two grinding worktables (17A, 17B) which undergo NC controlled movement or angularly controlled rotation independently of each other; and wherein the grinding head undergoes NC controlled movement in correspondence with the two grinding worktables (17A, 17B), wherein the two grinding worktables (17A, 17B) alternately move in a planar coordinate system in cooperation with the grinding head and alternately repeat operation in which while one of the grinding worktables, while holding a bend-broken glass plate, is effecting grinding of peripheral edges of the bend-broken glass plate by the grinding head, another one of the grinding worktables effects an operation of discharging a ground glass plate and receiving a next glass plate, to thereby allow the grinding head to effect grinding of consecutively received glass plates on a continual basis, wherein either: (a) said two grinding worktables (17A, 17B) move independently of each other in a Y-axis direction perpendicular to a direction of transporting the glass plate and are arranged in the transporting direction of the glass plate; and wherein said grinding head is adapted to move in an X-Y planar coordinate system in a changing manner with the grinding worktable holding the glass plate and effect grinding on a continual basis; or (b) said two grinding worktables (17A, 17B) are adapted to undergo angularly controlled rotation independently of each other and move in a Y-axis direction perpendicular to a transporting direction of the glass plate; and said grinding head is adapted to move in a planar coordinate system alternately in cooperation with each of the two grinding worktables (17A, 17B), the two grinding worktables being arranged in series in the transporting direction of the glass plate. (a) said two grinding worktables (17A, 17B) move independently of each other in a Y-axis direction perpendicular to a direction of transporting the glass plate and are arranged in the transporting direction of the glass plate; and wherein said grinding head is adapted to move in an X-Y planar coordinate system in a changing manner with the grinding worktable holding the glass plate and effect grinding on a continual basis; or (b) said two grinding worktables (17A, 17B) are adapted to undergo angularly controlled rotation independently of each other and move in a Y-axis direction perpendicular to a transporting direction of the glass plate; and said grinding head is adapted to move in a planar coordinate system alternately in cooperation with each of the two grinding worktables (17A, 17B), the two grinding worktables being arranged in series in the transporting direction of the glass plate.