A non-protruding connecting structure allowing zero to 360 degrees and any intermediate angle of relative rotation between two display screens includes a hinge assembly, a first shaft body, a second shaft body, and a fixing member. The hinge assembly includes first and second wheels sleeved on first and second shaft bodies, and an enmeshed worm engaged with the first and second wheels. A central axis of the first wheel is parallel to that of the second wheel. The axis of the worm is perpendicular to that of the first and second wheels. A rotation direction of the first wheel is opposite to that of the second wheel. The fixing member fixes the hinge assembly. An electronic device including the connecting structure is also disclosed.