The present invention relates to a method for producing graphene on a face-centered cubic metal catalyst having a plane oriented in one direction, and more particularly to a method of producing graphene on a metal catalyst having the (100) or (111) crystal structure and a method of producing graphene using a catalyst metal foil having a single orientation, obtained by electroplating a metal catalyst by a pulse wave current and annealing the metal catalyst. The invention also relates to a method of producing graphene using a metal catalyst, and more particularly to a method of producing graphene, comprising the steps of: alloying a metal catalyst with an alloying element; forming step structures on the metal catalyst substrate in an atmosphere of a gas having a molecular weight of carbon; and supplying hydrocarbon and hydrogen gases to the substrate. On unidirectionally oriented metal catalyst prepared according to the present invention, graphene can be grown uniformly and epitaxially. Moreover, a method for producing graphene according to the present invention can form monolayer graphene by epitaxially growing graphene while increasing the growth rate of graphene.