Abstract: The coin wrapping machine of the present invention comprises a coin feeding device for feeding a plurality of coins one by one; a stacking device for stacking the fed coins; a wrapping paper winding and clamping device for performing a wrapping operation to produce wrapped stacks of coins by winding a wrapping paper around the circumference of the stacked coins, and clamping the wrapping paper by a pair of upper and lower clamping nails by moving the respective nails upwardly and downwardly; an insufficient/excess number detecting device for detecting an insufficient or excess number of the wrapped stack of coins; and a wrapping paper multiple winding control device for directing the wrapping paper winding and clamping device to perform the wrapping operation twice or more for the wrapped stack of coins when the insufficient or excess number of coins is detected by an insufficient/excess number detecting device.