Control synthesis of high quality large-area graphene on transition metals (TMs) by chemical vapor deposition (CVD) is the most fascinating approach for practical device applications. Interaction of carbon atoms and TMs is quite critical to obtain graphene with precise layer number, crystal size and structure. Here, we reveal a solid phase reaction process to achieve Cu assisted graphene growth in nanoscale by in-situ transmission electron microscope (TEM). Significant structural transformation of amorphous carbon nanofiber (CNF) coated with Cu is observed with an applied potential in a two probe system. The coated Cu particle recrystallize and agglomerate toward the cathode with applied potential due to joule heating and large thermal gradient. Consequently, the amorphous carbon start crystallizing and forming sp(2) hybridized carbon to form graphene sheet from the tip of Cu surface. We observed structural deformation and breaking of the graphene nanoribbon with a higher applied potential, attributing to saturated current flow and induced Joule heating. The observed graphene formation in nanoscale by the in-situ TEM process can be significant to understand carbon atoms and Cu interaction.