Reasonable design of effective and durable electrocatalysts for methanol oxidation reaction (MOR) is crucial for promoting the commercialization of direct methanol fuel cells (DMFCs). In this work, a network-like PtCu structure supported on three-dimensional N-doped graphene-carbon nanotube (n-PtCu/3DNG-CNT) was successfully prepared via a rational design strategy. The three-dimensional N-doped graphene with an open porous structure facilitates methanol molecule transfer, exposes activity sites, and anchors metal catalysts effectively. The designed network-like PtCu structure, with lattice defects, steps, and twin grain boundaries, is befeficial for inducing new properties (lattice structure, electronic structure, and chemical structure), forming more effective active centers while enhancing its anti-CO poisoning ability through a bifunctional mechanism. Further characterizations reveal the existence of a complex interface effect between N-doped graphene and carbon nanotube, which is demonstrated in detail. The n-PtCu/3DNG-CNT catalyst exhibits excellent MOR activity and durability in an acidic medium.