In this paper, we studied the dependence of adhesion between CVD graphene and copper substrate on different crystallographic orientations of copper grains. It was determined that the adhesion between graphene and copper surface increases for grains with low-index crystallographic orientations. This phenomenon is explained by the surface microrelief formation during the crystallization of the copper surface layer, molten at the stage of annealing and graphene growth. During the liquid layer cooling and crystallizing, partial exfoliation of graphene from the copper surface occurs. Graphene exfoliation leads to an increase in defectiveness of the graphene layer. However, graphene peeling from copper grains with high-index crystallographic orientations can significantly reduce damage to graphene during the transfer process to a polymer surface.