The　direct　observation　of　single　crystal　graphene　growth　and　its　shape　evolution　is　of　fundamental　importance　to　the　understanding　of　graphene　growth　physicochemical　mechanisms　and　the　achievement　of　wafer-scale　single　crystalline　graphene.　Here　we　demonstrate　the　controlled　formation　of　single　crystal　graphene　with　varying　shapes,　and　directly　observe　the　shape　evolution　of　single　crystal　graphene　by　developing　a　localized-heating　and　rapid-quenching　chemical　vapor　deposition　(CVD)　system　based　on　electromagnetic　induction　heating.　Importantly,　rational　control　of　circular,　hexagonal,　and　dendritic　single　crystalline　graphene　domains　can　be　readily　obtained　for　the　first　time　by　changing　the　growth　condition.　Systematic　studies　suggest　that　the　graphene　nucleation　only　occurs　during　the　initial　stage,　while　the　domain　density　is　independent　of　the　growth　temperatures　due　to　the　surface-limiting　effect.　In　addition,　the　direct　observation　of　graphene　domain　shape　evolution　is　employed　for　the　identification　of　competing　growth　mechanisms　including　diffusion-limited,　attachment-limited,　and　detachment-limited　processes.　Our　study　not　only　provides　a　novel　method　for　morphology-controlled　graphene　synthesis,　but　also　offers　fundamental　insights　into　the　kinetics　of　single　crystal　graphene　growth.