Based on the π-electron energy dispersion relation of general compound lattices derived from the tight-binding model, and assuming that the transverse confinement potential of graphene nanoribbon is a infinite hard-wall potential，we obtain the energy dispersion relation of graphene nanoribbon and the conditions that determine whether it is metallic or semi-conducting. The results presented here show that the electronic structure of graphene nanoribbon is intimately related to its geometric structure （symmetry and width），so graphene nanoribbon can be modified as metallic or semi-conducting materials only by controlling its geometric configurations，which suggests that it is highly promising to use graphene nanoribbon to develop novel nano-scale devices.