The dynamics of the focusing of laser-driven ion beams produced from concave solid targets was studied. Most of the ion beam energy is observed to converge at the center of the cylindrical targets with a spot diameter of 30 μm, which can be very beneficial for applications requiring high beam energy densities. Also, unbalanced laser irradiation does not compromise the focusability of the beam. However, significant filamentation occurs during the focusing, potentially limiting the localization of the energy deposition region by these beams at focus. These effects could impact the applicability of such high-energy density beams for applications, e.g., in proton-driven fast ignition.