Density functional theory (DFT) calculation is employed to study the adsorption properties of Pb and Cu on recently synthesized two-dimensional materials MXenes, including Ti₃C₂, V₂C₁ and Ti₂C₁. The influence of surface decoration with functional groups such as H, OH and F have also been investigated. Most of these studied MXenes exhibit excellent capability to adsorb Pb and Cu, especially the adsorption capacity of Pb on Ti₂C₁ is as high as 2560 mg g⁻¹. Both the binding energies and the adsorption capacities are sensitive to the functional groups attached to the MXenes' surface. Ab initio molecular dynamics (ab-init MD) simulation confirms that Ti₂C₁ remains stable at room temperature after adsorbing Pb atoms. Our calculations imply that these newly emerging two-dimensional MXenes are promising candidates for wastewater treatment and ion separation.