PROBLEM TO BE SOLVED: To provide a balloon wrapping machine and a balloon wrapping method capable of accurately positioning a balloon to a pleating part and a folding part, and inserting the balloon.SOLUTION: A balloon wrapping machine for wrapping a balloon 52 of a balloon catheter 50 having the balloon 52 at the tip of a long shaft 51 includes: a pleating part 2 for forming a blade shape to the balloon 52; a folding part 3 for folding the blade shape formed to the balloon 52 along the circumferential direction; and a support part 4 for supporting the balloon catheter 50 and causing the tip of the shaft 51 including the balloon 52 to be freely inserted into the pleating part 2 and the folding part 3. Both the pleating part 2 and the folding part 3 are vertically arranged so as to insert the balloon 52 in a vertical direction.SELECTED DRAWING: Figure 2