The nucleation and growth kinetics of multilayered graphene on Cu substrates in low pressure chemical vapor deposition is investigated. Uniform millimeter-sized single crystalline graphene grains are formed under high temperature and high hydrogen to methane ratio conditions. Moreover, beneath each first layered grain, we found numerous multi-layered adlayer grains with wide size distribution. Through Raman spectroscopy, atomic force microscopy, and image processing, we quantitatively characterize the graphene growth. We show evidence for non-equilibrium growth kinetics in the adlayer, in contrast to the equilibrium growth kinetics of the first layer. The out-diffused carbon sources from the bulk of catalyst plays important role in the multi-layered graphene growth through generation of new nucleation sites underneath the first layer during the whole growth process. Balance between the role of hydrogen as catalysis and etchant, and the capping area of first layer, are shown to be important factors in determining the eventual multilayer characteristics.