A reversing transmission includes a shaft, a retainer, a spacing collar, reversing members, two gears and two covers. The holder is sleeved on the shaft with spaced sliding notches formed thereon. The spacing collar is mounted on an outer surface of the retainer. The reversing members each include two spaced swing plates, with two reversed spiral teeth dented on two diagonal half surfaces of the two spaced swing plates. The reversing members slide into the sliding notches of the holder, with the two swing plates of each reversing member distributed at different sides of the spacing collar. Each of the gears has a group of spiral teeth formed on the inner side for engaging with the group of spiral teeth of the reversing members, and cogs formed on the outer circumference surface. The covers are mounted on two opposite ends of the holder to keep the reversing members in position.