A generally covariant formulation is made for the previously proposed unified model of the Nambu-Jona-Lasinio type for gravity and electromagnetism. The gravitational and electro-magnetic fields are generated as collective excitations of fermion-antifermion pairs. The modl is shown to be effectively equivalent to the Einstein-Weyl theory of general relativity. The G-α relation, the relation between the fine structure constant and the Newtonian gravitational constant is re-derived.