Carbon solid solubility in metals is an important factor affecting uniform graphene growth by chemical vapor deposition (CVD) at high temperatures. At low temperatures, however, it was found that the carbon diffusion rate (CDR) on the metal catalyst surface has a greater impact on the number and uniformity of graphene layers compared with that of the carbon solid solubility. The CDR decreases rapidly with decreasing temperatures, resulting in inhomogeneous and multilayer graphene. In the present work, a Ni–Cu alloy sacrificial layer was used as the catalyst based on the following properties. Cu was selected to increase the CDR, while Ni was used to provide high catalytic activity. By plasma-enhanced CVD, graphene was grown on the surface of Ni–Cu alloy under low pressure using methane as the carbon source. The optimal composition of the Ni–Cu alloy, 1:2, was selected through experiments. In addition, the plasma power was optimized to improve the graphene quality. On the basis of the parameter optimization, together with our previously-reported, in-situ, sacrificial metal-layer etching technique, relatively homogeneous wafer-size patterned graphene was obtained directly on a 2-inch SiO2/Si substrate at a low temperature (~600 °C).