The growth of large-domain single crystalline graphene with the controllable number of layers is of central importance for large-scale integration of graphene devices. Here we report a new pathway to greatly reduce the graphene nucleation density from ~10(6) to 4 nuclei cm(-2), enabling the growth of giant single crystals of monolayer graphene with a lateral size up to 5 mm and Bernal-stacked bilayer graphene with the lateral size up to 300 μm, both the largest reported to date. The formation of the giant graphene single crystals eliminates the grain boundary scattering to ensure excellent device-to-device uniformity and remarkable electronic properties with the expected quantum Hall effect and the highest carrier mobility up to 16,000 cm(2) V(-1) s(-1). The availability of the ultra large graphene single crystals can allow for high-yield fabrication of integrated graphene devices, paving a pathway to scalable electronic and photonic devices based on graphene materials.