Metal liner implosions driven by a pulsed current generator are used in research on inertial confinement fusion, generation of soft x-ray pulses and megagauss magnetic fields. The energy density in the plasma column formed during the liner stagnation is largely determined by the initial radius and the radial convergence of the liner. When the liner implosion time is close to the current rise time, the liner initial radius is proportional to the current rise time. The paper presents the results of experiments on the fast implosion of cylindrical liners on the MIG generator (2 MA, 80 ns) at the Institute of High Current Electronics, Tomsk, Russia. Liners 0.7–1.0 mm in diameter were made from a 1.8 to 2.5 μm thick aluminum foil. A low-density plasma was pre-injected into the liner area. As the Lorentz force sweeps away the pre-injected plasma, the current switches to the liner in 1–3 ns. Then the liner is imploded in 3–7 ns by a current close to the peak generator current. The stagnation radius measured via time-integrated pinhole camera images was found to be not more than 25 µm. Such a radius of the stagnated plasma assumes that the plasma mass density is several times higher than the solid aluminum density.