The structure of a tube expander has a ring and a bearing in the body thereof. An axle goes through the body. A driving head is connected to the axle on the body. The bottom of the axle has a guiding pin and a tapered head. The driving head has an external thread so that it can be rotated into the internal thread of the ring or rotated in the opposite direction out of the internal thread. A compressible elastic element is disposed inside the body and mounted on the axle. The top end of the compressible elastic element urges against the bottom of the ring. The bottom of the compressible elastic element pushes the guiding pin downward so that the external thread becomes idle after being completely rotated out of the internal thread.