A clamp structure for a tonneau cover of a pick-up truck is disclosed and mounted to one frame section of a tonneau cover for releasably securing the frame section on a side wall of a cargo bed of the pick-up truck. The clamp structure has a composite grip element which has a metal grip body and a plastic sleeve. The metal grip body has an engaging portion to stably engage with the side wall of the pick-up truck. The plastic sleeve has a first abutment flange to smoothly abut against a turning handle, and a second abutment end facing a sliding block. Thus, the composite grip element can provide advantages of both of metal and plastic material, so that the operational stability and reliability of the clamp structure can be enhanced, and the lifetime thereof can be elongated.