Involving oxygen in the traditional chemical vapor deposition (CVD) process has proven a promising approach to achieve large-scale graphene single crystals (GSCs), but its many relevant fundamental aspects are still not fully understood. Here we report a systematic study on the role of hydrogen in the growth of millimeter-sized GSCs using enclosure-like Cu structures via the oxygen-assisted CVD process. Results show that GSCs have different first layer growth behaviors on the inside and outside surfaces of a Cu enclosure when the H2 environment is varied, and these behaviors will consequently and strongly influence the adlayer formation in these GSCs, leading to two entirely different growth modes. Low H2 partial pressure (PH2) tends to result in fast growth of dendritically shaped GSCs with multiple small adlayers, but high PH2 can modify the GSC shape into hexagons with single large adlayer nuclei. This difference of adlayers is attributed to the different C diffusion paths determined by the shapes of their host GSCs. On the basis of these observations, we developed an isothermal two-step method to obtain GSCs with significantly improved growth rate and sample quality, in which low PH2 is first set to accelerate the growth rate followed by high PH2 to restrict the adlayer nuclei. Our results prove that the growth of GSCs can reach a reasonable optimization between their growth rates and sample quality by simply adjusting the CVD H2 environment, which we believe will lead to more improvements in graphene synthesis and fundamental insight into the related growth mechanisms.