Polyvinyl alcohol (PVA) composite materials made by mixing graphene and carbon nanotubes (CNTs) without chemically bonding them resulted in severe coagulation and deteriorated rigidity and ductility. We succeeded in improving the rigidity and ductility by proposing a G-CNT/PVA material fabricated by combining graphene and CNTs bonded through amide functionality. The proposed G-CNT/PVA has strength, rigidity, and ductility values of 24.0 MPa, 0.99 GPa, and 148.0%, respectively, at a nanocarbon content of 10 wt%. The electric resistance of the proposed G-CNT/PVA composite could be increased drastically by chemical bonding, while the nanocarbon (graphene, CNT) PVA composite materials, which had conventionally been conductive, now had sheet resistances of 87.02-0.300 k Omega/a-. The G-CNT/PVA composite was found to have similar strength, rigidity, and ductility to conventional nanocarbon materials, whilst dramatically increasing resistivity; thereby, the G-CNT/PVA can be a suitable candidate for insulators of stretchable devices and conductive nanocarbon materials.