We report molecular dynamics simulation of the (overall neutral) system consisting of an immobile macroion surrounded by the electrolyte of multivalent counterions and monovalent coions. In a short time (< a few nanoseconds), counterions adsorb on the macroion surface in the amount much exceeding neutralization requirement, thus effectively inverting the sign of the macroion charge. We find two conditions necessary for charge inversion, namely, counterions must be multivalently charged and Coulomb interactions must be strong enough compared to thermal energy. On the other hand, coion condensation on the multivalent counterions similar to Bjerrum pairing is the major factor restricting the amount of charge inversion. Depending on parameters, we observe inverted charge up to about 200% the original charge of the macroion in absolute value. The inverted charge scales as similar to zeta (1/2) when zeta <1 and crosses over to similar to zeta for zeta >1, where zeta=(A(0)/r(s))(2), r(s) is the Debye screening length in the electrolyte and A(0) is the distance between adsorbed counterions under neutralizing conditions. These findings are consistent with the theory of "giant charge inversion" [Phys. Rev. Lett. 85, 1568 (2000)].