Bernal-stacked (AB-stacked) bilayer graphene is of significant interest for functional electronic and photonic devices due to the feasibility to continuously tune its band gap with a vertical electric field. Mechanical exfoliation can be used to produce AB-stacked bilayer graphene flakes but typically with the sizes limited to a few micrometers. Chemical vapor deposition (CVD) has been recently explored for the synthesis of bilayer graphene but usually with limited coverage and a mixture of AB- and randomly stacked structures. Herein we report a rational approach to produce large-area high-quality AB-stacked bilayer graphene. We show that the self-limiting effect of graphene growth on Cu foil can be broken by using a high H(2)/CH(4) ratio in a low-pressure CVD process to enable the continued growth of bilayer graphene. A high-temperature and low-pressure nucleation step is found to be critical for the formation of bilayer graphene nuclei with high AB stacking ratio. A rational design of a two-step CVD process is developed for the growth of bilayer graphene with high AB stacking ratio (up to 90%) and high coverage (up to 99%). The electrical transport studies demonstrate that devices made of the as-grown bilayer graphene exhibit typical characteristics of AB-stacked bilayer graphene with the highest carrier mobility exceeding 4000 cm(2)/V · s at room temperature, comparable to that of the exfoliated bilayer graphene.