Graphene domains in different shapes have been grown on copper substrates via atmospheric pressure chemical vapour deposition by controlling the growth process parameters. Under stabilized conditions, graphene domains tend to be six-fold symmetric hexagons under low flow rate methane with some domains in an irregular hexagonal shape. After further varying the growth duration, methane flow rate, and temperature, graphene domains have developed shapes from hexagon to shovel and dendrite. Two connecting modes, through overlap and merging of adjacent graphene domains, are proposed.