A self-adaptive expansion sleeve comprises an inner sleeve body and an outer sleeve body, the outer sleeve body is arranged on the outer side of the inner sleeve body in a sleeving mode, a second end plate is arranged at the top of the outer sleeve body, a first end plate penetrating through the second end plate is arranged at the top of the inner sleeve body, and a plurality of first bolt holes are formed in the first end plate; the first end plate is provided with first bolt holes, the second end plate is provided with second bolt holes matched with the first bolt holes in position and number, bolts are correspondingly installed in the first bolt holes and the second bolt holes, the first end plate and the second end plate are each provided with a first adapting groove, and the side wall of the inner sleeve body is provided with a plurality of second adapting grooves in the axial direction. A plurality of grooves are formed in the inner wall of the inner sleeve body in the axial direction, rubber strips are embedded in the grooves, and a third adapting groove is formed in the outer sleeve body in the axial direction. The connecting device can adapt to the connection of shafts with more specifications and hubs, and can adapt to the connection of shafts with more types, so that the connection stability is improved.