Pt-based alloy or bimetallic anode catalysts have been developed to reduce the carbon monoxide (CO) poisoning effect and the usage of Pt in direct methanol fuel cells (DMFCs), where the second metal plays a role as CO poisoning inhibitor on Pt. Furthermore, better performance in DMFCs can be achieved by improving the catalytic dispersion and using high-performance supporting materials. In this work, we introduced a free-standing, macroscopic, interwoven tubular graphene (TG) mesh as a supporting material because of its high surface area, favorable chemical inertness, and excellent conductivity. Particularly, binary AuPt nanoparticles (NPs) can be easily immobilized on both outer and inner walls of the TG mesh with a highly dispersive distribution by a simple and efficient chemical reduction method. The TG mesh, whose outer and inner walls were decorated with optimized loading of binary AuPt NPs, exhibited a remarkably catalytic performance in DMFCs. Its methanol oxidation reaction (MOR) activity was 10.09 and 2.20 times higher than those of the TG electrodes with only outer wall immobilized with pure Pt NPs and binary AuPt NPs, respectively. Furthermore, the catalyst also displayed a great stability in methanol oxidation after 200 scanning cycles, implying the excellent tolerance toward the CO poisoning effect.