It is intended in an apparatus for successively making plastic bags that a plastic film 1 is cut by a Thomson blade 3 without making the Thomson blade 3 pressed with a large force. The Thomson blade 3 is brought into contact with the plastic film 1 on one of opposite sides of the plastic film 1 in a direction of thickness thereof while a rolling member 4 is brought into contact with the plastic film 1 and rolled and moved along the plastic film 1 and the Thomson blade 3 on the other side of the plastic film 1 in the direction of thickness thereof. The plastic film 1 is therefore sandwiched between and cut by the Thomson blade 3 and the rolling member 4 to successively make plastic bags.