The effect of substitutional impurities as Zinc (Zn), Cadmium (Cd) and Mercury (Hg) on electronic properties of graphene nanoribbons (GNRs) was investigated by using Density Functional Theory ( DFT). A substantial change in the electronic properties of GNR structures was observed while changing the position of dopant atom from the edge to the center of armchair graphene nanoribbons (AGNRs) and zigzag graphene nanoribbons (ZGNRs). The calculations are shown that the electronic band gap of GNRs can be controlled depending on the position of dopant atoms. The calculated electronic band structures for both AGNRs and ZGNRs show spin-dependent metallic or semiconductor behavior according to the position of dopant atoms. From the Density of States ( DOS) information, quasi-zero-dimensional (Q0D) and quasi-one-dimensional (Q1D) type behaviors are observed. It is shown that because the doped ZGNRs had the lowest total energies, ZGNRs are energetically more stable than AGNRs.