The growth of high-quality graphene on copper substrates has been intensively investigated using chemical vapor deposition (CVD). It, however, has been considered that the growth mechanism is different when graphene is synthesized using a plasma CVD. In this study, we demonstrate a dual role of hydrogen for the graphene growth on copper using an inductively coupled plasma (ICP) CVD. Hydrogen activates surface-bound carbon for the growth of high-quality monolayer graphene. In contrast, the role of an etchant is to manipulate the distribution of the graphene grains, which significantly depends on the plasma power. Atomic-resolution transmission electron microscopy study enables the mapping of graphene grains, which uncovers the distribution of grains and the number of graphene layers depending on the plasma power. In addition, the variation of electronic properties of the synthesized graphene relies on the plasma power.