Heavy metal (HM) pollution is of great concern currently because it has been recognized as a potential threat to air, water,and soil. Adsorption is one of the most effective strategies for removing heavy metals. Montmorillonite as the adsorbent with a low cost and high thermal stability has received much attention. The adsorption of heavy metal Copper [Cu(II)] and Plumbum [Pb(II)] atoms on Na-montmorillonite hydroxylated (010) edge surface was analyzed using the generalized gradient approximation and density functional theory in the supercell technique. The coverage dependence of the adsorption structure and energetics was systematically investigated for a wide range of coverage from 0 to 1.0 monolayer (ML). Among all the possible adsorption sites, the most stable adsorption site for Cu(II) atom was a three-fold hollow site while the most favorable adsorption site for Pb(II) atom was a three-fold hollow site and followed by a two-fold bridge site. The adsorption energy increased with increasing coverage of Pb(II) atoms, indicating higher stability of surface adsorption and a tendency for the formation of adsorbate island clusters with increasing coverage. However, the adsorption energy of Cu(II) atoms decreased with increasing coverage. In the coverage range of 0 < Θ ≤ 0.5 ML the recovery capacity of the Na-montmorillonite for the heavy metal atoms was in the order of Cu(II)>Pb(II), while the recovery capacity of the Na-montmorillonite in the coverage range of 0.5 < Θ ≤ 1 ML was in the order of Pb(II)>Cu(II). The other aspects of the Cu(II) and Pb(II)/Na-montmorillonite (010) systems, including adsorption geometry, differential charge distribution, and electronic density of states were also studied and discussed in detail.