The acceleration of super-heavy ions from an ultra-thin lead target irradiated by a femtosecond laser pulse with an intensity in the range of ∼1022–1023 W cm−2 was investigated using an advanced 2D3V particle-in-cell code. It is shown that by properly selecting the laser pulse parameters, it is possible to produce a practically single-charge Pb ion beam with multi-GeV ion energies and the laser-to-ions energy conversion efficiency approaching 30%. At the laser intensity of 1023 W cm−2, Pb ions with the charge state Z = 72 carry over 90% of the total energy of all ions, while the peak intensity and peak fluence of the Pb+72 ion beam are at least two orders of magnitude higher than for other types of ions. In addition, the Pb+72 ion beam is more compact and has a smaller angular divergence than those for other types of ions. The above properties of the Pb+72 ion beam mean that further energy-efficient purification of the beam from other types of ions is possible, even in simple ion transport and selection systems.