In this study, electronic properties of graphene nanoribbons with armchair edges (AGNRs) have been investigated with Density Functional Theory (DFT). Effects of heavy metal (HM) elements, including Zinc (Zn), Cadmium (Cd) and Mercury (Hg) atoms on electronic behavior of AGNRs have been calculated by passivating for both one and two edges of AGNRs in detail. To explain the electronic behavior of investigated AGNRs, the electronic band structure, the density of states (DOS), total energy have been calculated. Energetically favorable structures have been determined using calculated binding energy values. The obtained bandgap values of investigated structures changes between 0.30 and 0.64 eV. Increasing atomic number of passivation atoms have led to an increment in the bandgap of AGNRs.