A wrapper for wrapping bales of crop material includes a frame, a wrapping table, a wrapping device, and a loading device. The loading device includes a pivotable loading structure, and at least one actuator to move the loading structure between a pick-up position and a release position, wherein the loading structure comprises two loading arms between which the bale can be arranged. A pivotable grip arm is mounted on each loading arm. The pivotable grip arms are pivotable with respect to the loading arms between a closed position and an open position, and the at least one actuator is arranged to also move at least one of the grip arms between the open and the closed position.