A nonvolatile memory device includes a memory cell array; and a high voltage generator arranged to generate a high voltage to be supplied to the memory cell array. The high voltage generator includes a pump unit block having a plurality of pump units supplied with an external voltage and at least one of the pumps is engaged in pumping the external voltage to a higher, output, voltage, at a steady clock rate. The number of pumps engaged in pumping is increased until a predetermined period has elapsed. The rate at which the number of pumps is increased depends upon the value of the external voltage.