A single-layer graphene is synthesized on Cu foil in the absence of H(2) flow by plasma enhanced chemical vapor deposition (PECVD). In lieu of an explicit H(2) flow, hydrogen species are produced during the methane decomposition process into their active species (CH(x<4)), assisted with the plasma. Notably, the early stage of growth depends strongly on the plasma power. The resulting grain size (the nucleation density) has a maximum (minimum) at 50 W and saturates when the plasma power is higher than 120 W because hydrogen partial pressures are effectively tuned by a simple control of the plasma power. Raman spectroscopy and transport measurements show that decomposed methane alone can provide a sufficient amount of hydrogen species for high-quality graphene synthesis by PECVD.