Although the success of graphene research has opened up a new route for wearable electronic and optoelectronic devices, producing graphene with controllable quality and cost-effective growth on a large scale remains challenging due to the lack of understanding about its growth kinetics. Domain boundaries interrupt lattice continuity of graphene; therefore, lowering the nucleation density at the initial stage of graphene growth in the chemical vapor deposition (CVD) process is beneficial for improving the quality of graphene for applications. Herein, we show that by forming an oxide passivation layer on Cu substrates before CVD graphene growth, graphene nucleation density can be effectively decreased. The nucleation mechanism in the presence of an oxide passivation layer is of interest. The analysis of graphene growth kinetics suggests that the thickness of the boundary layer for mass transfer on the substrate surface plays an important role in controlling the reduction rate of the oxide passivation layer. A thick boundary layer created under slow gas flow causes slow reduction of the oxide passivation layer, making finite sites for graphene nucleation. The domain density in a graphene layer is therefore significantly reduced. Graphene sheets of various domain densities (ranging from 104 to 1 mm-2) can be fabricated by suitably choosing the growth parameters. The graphene sheet with a lower density of domain boundaries exhibits better electrical conductivities.