The design of neural electrodes has changed in the past decade, driven mainly by the development of new materials that open the possibility of manufacturing electrodes with adaptable mechanical properties and promising electrical properties. In this paper, we report on the mechanical and electrochemical properties of a polydimethylsiloxane (PDMS) composite with edge-functionalized graphene (EFG) and demonstrate its potential for use in neural implants with the fabrication of a novel neural cuff electrode. We have shown that a 200 μm thick 1:1 EFG/PDMS composite film has a stretchability of up to 20%, a Young's modulus of 2.52 MPa, and a lifetime of more than 10000 mechanical cycles, making it highly suitable for interfacing with soft tissue. Electrochemical characterization of the EFG/PDMS composite film showed that the capacitance of the composite increased up to 35 times after electrochemical reduction, widening the electrochemical water window and remaining stable after soaking for 5 weeks in phosphate buffered saline. The electrochemically activated EFG/PDMS electrode had a 3 times increase in the charge injection capacity, which is more than double that of a commercial platinum-based neural cuff. Electrochemical and spectrochemical investigations supported the conclusion that this effect originated from the stable chemisorption of hydrogen on the graphene surface. The biocompatibility of the composite was confirmed with an in vitro cell culture study using mouse spinal cord cells. Finally, the potential of the EFG/PDMS composite was demonstrated with the fabrication of a novel neural cuff electrode, whose double-layered and open structured design increased the cuff stretchability up to 140%, well beyond that required for an operational neural cuff. In addition, the cuff design offers better integration with neural tissue and simpler nerve fiber installation and locking.