An adjustable socket structure contains a body including a first groove, a second groove, a first notch, a number of slots; a plurality of paws, each including a sliding block, and the sliding block including a first hole; a number of connecting rods, each being movably fixed in the second groove and including a first axial shank and a second axial shank; a driving shaft including an axial portion and a disk portion, wherein the axial portion includes a square bore, and the disk portion is rotated in the first groove and includes an outer diameter larger that the axial portion and three second holes so that the driving shaft is rotated to actuate the paws to move in the slots respectively by using the connecting rods; a helical retaining ring retained in the first notch to abut against a rear end of the disk portion of the driving shaft.