The optimized growth parameters of graphene with different morphologies, such as dendrites, rectangle, and hexagon, have been obtained by low-pressure chemical vapor deposition on polycrystalline copper substrates. The evolution of fractal graphene, which grew on the polycrystalline copper substrate, has also been observed. When the equilibrium growth state of graphene is disrupted, its intrinsic hexagonal symmetry structure will change into a non-hexagonal symmetry structure. Then, we present a systematic and comprehensive study of the evolution of graphene with different morphologies grown on solid copper as a function of the volume ratio of methane to hydrogen in a controllable manner. Moreover, the phenomena of stitching snow-like graphene together and stacking graphene with different angles was also observed.