A pulsed hollow cathode glow discharge with current up to 200 A, with the pulse width amounting to a few milliseconds, is studied in a wide range of the gas pressure p from 0.01 to 10 Pa. The high current discharge is established due to the application of a high-voltage pulse with amplitude Uo up to 5 kV between the anode and the hollow cathode of a continuous discharge with a current of Io = 0.5 A. The establishing time τ ranges from 10 to 300 μs, diminishes with the pulse amplitude growth, increases in the gas pressure, and decreases in the output orifice area of the hollow cathode. At Uo > 2.5 kV, an abnormal mode of the discharge establishing process is observed with intensive oscillations of the discharge current and voltage in the frequency range from 1 to 10 MHz. In the abnormal mode, the high current establishing time τ can be reduced by hundred times down to τ ∼ 1 μs. At a low gas pressure p < 0.1 Pa, the high current can be reached only in the abnormal mode. Without oscillations at the pulse front, only low-current high-voltage discharge is established.