A theory is developed for calculating the charge composition of a cluster plasma produced upon irradiation of large atomic clusters by the field of a superatomic femtosecond laser pulse. The theory is based on the overbarrier process of a successive multiple internal ionization of atomic ions inside a cluster accompanied by the external field ionization. Collision ionization is also taken into account in the calculations. The theory is illustrated by the example of a cluster consisting of 10⁶ xenon atoms irradiated by a 50-fs laser pulse with a peak intensity of 2 × 10¹⁸ W/cm ². In this case, the Xe²⁶⁺ ions dominate. The amounts of atomic xenon ions with multiplicity up to 31 are calculated.