Abstract As is well established, mastery to precise control of the layer number, stacking order of graphene, and the size of single-crystal monolayer graphene is very important for both fundamental interest and practical applications. In this report, millimeter-sized single-crystal monolayer graphene has been synthesized to multilayer graphene on Cu by chemical vapor deposition. The relationship of the growth process between monolayer graphene and multilayer graphene is investigated carefully. Besides the general multilayer graphene with Bernal stacking order, parts of multilayer graphene with non-Bernal stacking order were modulated under optimized growth conditions. The oxide nanoparticle on the Cu surface derived from annealing has been found to play the key role in nucleation. In addition, the hydrogen concentration impacts significantly on the layer number and shape of the graphene. Moreover, a possible mechanism was proposed to understand the growth process discussed above, which may provide an instruction to graphene growth on Cu by chemical vapor deposition.