The invention relates to a robot gripper structure, which comprises a circular arc finger pair, a copper column, a front baffle plate, an upper end cover, a lower end cover and a tiller double connecting rod mechanism. The tiller double connecting rod mechanism is provided with a round tiller and two connecting rods; the two connecting rods are respectively coupled to symmetrical positions on the tiller, which are certain distances away from a circle center and take the circle center as a center; fingers which are vertical to a plane where the tiller is positioned and face the same direction are arranged at handle ends of the two connecting rods respectively so as to form the finger pair for clamping a workpiece; and the center of a disk is provided with a groove gear structure which can be coupled with a corresponding projecting gear on a driving structure and drives the disk through the gear structure so as to drive the fingers on the handles at the two ends of the connecting rods to move. The robot gripper has the advantages of simple structure, low cost, and suitability for mass production.