The present invention is to provide a wobble-resistant hinge structure, comprising a main frame body having a main plate; a first pivotal axle with one end of its axle rod being inserted with the main plate, at least a resilient plate body with a succession of wave or uneven surface, and a support part, and with the free end of the axle rod being capped, wherein the resilient plate body is disposed with at least a pair of flat portions and the support part corresponding to the flat portions s protrudingly to form a pair of support legs, which are held compressingly against the flat portions and are supported by the main plate, such that the application of external force on the resilient plate body will not result in wobbling.