A nanomaterial, a copper-based metal organic framework (Cu-BTC MOF), was prepared by a one-step solvothermal synthesis method and applied for the removal of Pb(II) ions from an aqueous solution via adsorption. The Cu-BTC MOF nanomaterial was characterized via X-ray diffraction, Fourier transform infrared, scanning electron microscopy (SEM), transmission electron microscopy (TEM), energy-dispersive X-ray spectroscopy (EDX), and Brunauer–Emmett–Teller method. TEM and SEM images of the prepared Cu-BTC MOF presented octahedral crystals. Furthermore, EDX spectroscopy showed that the synthesized porous nanomaterial consisted of Cu, O, and C elements. The prepared Cu-BTC MOF was employed as an adsorbent for the removal of Pb(II) ions from an aqueous solution. Adsorption kinetics and adsorption isotherm modeling were conducted in detail. The maximum adsorption capacity values of the Cu-BTC MOF for Pb(II) ions at temperature conditions of 10, 25, and 40 °C were 890.94, 896.04, and 958.37 mg/g, respectively. The synthesized Cu-BTC MOF showed high distribution coefficient (Kd) values, and it was very effective in extracting Pb(II) ions. In the Pb adsorption process, the molar ratio of Pb adsorption/Cu desorption was found to be close to 1 indicating that ion exchange with Cu ions in the Cu-BTC MOF material occurs and the cation exchange between Pb ions and Cu ions can be considered as a dominant mechanism of the adsorption.