Graphene produced by chemical vapor deposition (CVD) methods has been considered as a promising corrosion prevention layer because of its exceptional structure and impermeability. However, the anti-corrosion performance and the failure mechanism are still controversial. In this study, graphene layers with different quality levels, crystallite sizes, and layer numbers were prepared on the surface of Cu by a CVD process. The effects of grain boundaries (GBs) on the failure of graphene layers to provide adequate protection were investigated in detail by combining graphene transfer techniques, computation, and anti-corrosion measurements. Our results reveal that corrosion rates decrease marginally upon the increase of graphene layer number, and this rather weak dependence on thickness likely arises from the aligned nature of the GBs in CVD-grown few-layer graphene. This problem can potentially be overcome by layer-by-layer graphene transfer technique, in which corrosion is found to be arrested locally when transferred graphene is present on top of the as-grown graphene. However, this advantage is not reflected in corrosion studies performed on large-scale samples, where cracks or imperfect interfaces could offset the advantages of GB misalignment. With improvements in technology, the layer-by-layer assembly technique could be used to develop an effective anti-corrosion barrier.