Hexagonal boron nitride (h-BN) has received a great deal of attention as a substrate material for high-performance graphene electronics because it has an atomically smooth surface, lattice constant similar to that of graphene, large optical phonon modes, and a large electrical band gap. Herein, we report the large-scale synthesis of high-quality h-BN nanosheets in a chemical vapor deposition (CVD) process by controlling the surface morphologies of the copper (Cu) catalysts. It was found that morphology control of the Cu foil is much critical for the formation of the pure h-BN nanosheets as well as the improvement of their crystallinity. For the first time, we demonstrate the performance enhancement of CVD-based graphene devices with large-scale h-BN nanosheets. The mobility of the graphene device on the h-BN nanosheets was increased 3 times compared to that without the h-BN nanosheets. The on–off ratio of the drain current is 2 times higher than that of the graphene device without h-BN. This work suggests that high-quality h-BN nanosheets based on CVD are very promising for high-performance large-area graphene electronics.