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.