Vertically-oriented graphene (VG) with predominantly edge plane structure is considered as a promising catalyst support candidate for the methanol oxidation reaction (MOR) in direct methanol fuel cells (DMFCs). Inspired by the fact that catalyst nanoparticles are spontaneously attached to the exposed graphene edges, a novel highly-branched vertically-oriented graphene (HBVG) based catalyst support is proposed in the current work. With employing atmospheric normal glow discharge (ANGD) and microwave plasma-enhanced chemical vapor deposition (PECVD) methods, HBVG and maze-like VG (MVG) are synthesized on the surface of carbon paper (CP), respectively. Pt nanoparticles are deposited on pristine CP, HBVG-CP, and MVG-CP with the same route of repeated double-potential pulse electrodeposition (RDPE). Experimental results show that HBVG-CP with dense open graphitic edge planes can desirably provide a considerable number of nuclei sites for the fast nucleation and well dispersion of Pt nanoparticles. Meanwhile, a certain amount of oxygen-containing functional groups on the HBVG surface will benefit the rapid removal of CO and accumulated carbonaceous species. Based on the electrochemical measurements on Pt utilization efficiency, catalytic activity, CO tolerance, and long-term stability, Pt/HBVG-CP is demonstrated to be able to present enhanced catalytic performance over the Pt/CP and Pt/MVG-CP counterparts, holding a great potential for fuel cell applications.