Large area graphene sheets grown by chemical vapor deposition can potentially be employed as a transparent electrode in photovoltaics if their sheet resistance can be significantly lowered, with minimal loss in transparency. Here, we report the fabrication of a graphene-conducting-carbon-nanotube (CCNT) hybrid material with a sheet resistance considerably lower than neat graphene, and with the requisite small reduction in transparency. Graphene is deposited on top of a a self-assembled CCNT monolayer which creates parallel conducting paths on the graphene surface. The hybrid thereby circumvents electron scattering due to defects in the graphene sheet, and reduces the sheet resistance by a factor of two. The resistance can be further reduced by chemically doping the hybrid. Moreover, the chemically doped hybrid is more stable than a standalone chemically doped graphene sheet, as the CCNT network enhances dopant binding. In order to understand the results, we develop a 2D resistance network model in which we couple the CCNT layer to the graphene sheet and demonstrate the model accounts quantitatively for the resistance decrease. Our results show that a graphene-CCNT hybrid system has high potential for use as a transparent electrode in photovoltaic applications.