The recent progress of graphene oxide (GO), it is considered as the most promising nano adsorbents for water purification. In this study, the adsorption potentiality of this nano material was increased by functionalization of graphene with chloroacetic acid (GO/CAA). The potentiality was evaluated by applying GO and GO/CAA in the removal of lead (Pb) from synthetic waste water. The analyses of FTIR spectroscopy, X-ray diffraction patterns, and scanning electron microscope supported to the successful preparation of GO/CAA from GO. In case of adsorption of Pb (II) by GO and GO/CAA, Langmuir adsorption isotherm indicated more fit for describing the Pb (II) adsorption. According to the Langmuir adsorption isotherm, the maximum adsorption capacities ($qe$) of GO and GO/CAA were found 0.25 and 0.52 ​mol/g, respectively. The pseudo second order model displayed higher correlation and hence elucidates the reaction kinetics well with both GO and GO/CAA. Molecular level insights obtained from the molecular dynamics study proved that the studied GO shows excellent adsorption efficiency to the Pb2+ ions by the intermolecular interactions among the Pb cations and oxygen atoms of the GO surface, where anions of the lead compounds could help Pb2+ ions to form clusters around GO layers. Overall, this study suggests that the modification of GO exposed higher potentiality in the purification of Pb (II).