A hybrid structure (HS) made of one-dimensional ZnO nanorods (NRs) and a two-dimensional synthesized graphene sheet was successfully constructed in this study. The uniform ZnO NRs were obtained by hydrothermal method and grown on a graphene surface that had been transferred to a polyethylene terephthalate substrate. The HS exhibited high transmittance (approximately 75%) over the visible wavelength range, even after cyclic bending with a small radius of curvature. Raman spectroscopy and Hall measurement were carried out to verify the chemical composition and electrical properties of the structure. Stable electrical conductance of the ZnO NR/graphene HS was achieved, and increase in carrier mobility decreased the resistance of the ZnO-with-graphene sheet in comparison with bare ZnO NRs.