Understanding the fundamentals of chemical vapor deposition bilayer graphene growth is crucial for its synthesis. By employing density functional theory calculations and classical molecular dynamics simulations, we have investigated the evolution of carbon structures and the kinetics of the adlayer graphene nucleation between the graphene top layer (GTL) and the Ni(111) substrate. Compared to the epitaxial GTL, the weaker interaction between the nonepitaxial GTL and the Ni(111) substrate makes the nucleation of the adlayer more favorable. Furthermore, the defects involving in the adlayer graphene are easier to be healed by adopting the nonepitaxial GTL. Our results agree well with the experimental observation and demonstrate that the adlayer graphene with a high quality can be grown underneath the nonepitaxial GTL on Ni-like substrates.