The electric charge transport through the two-grid systems of the Alternative Low Power Ion Engine is studied using a particle-in-cell (PIC) code. In this plasma thruster design, the ionizing electrons from the only cathode and the ions extracted from the ionization chamber flow in opposite directions through the open spaces of its grids. This configuration differs from classical gridded ion engines where only positive ions are accelerated. The electric charge transport is simulated, and the results are in agreement with previous experimental observations. The numerical simulations are performed for a single beamlet domain in a 2D axial symmetry, and only two aligned holes of the grid system are studied. The extracted ions move outwards from the ionization chamber reaching supersonic velocities of 43–51 km/s which are controlled by an acceleration voltage. The ionizing electrons from the only cathode are accelerated along the opposite direction and achieve energies in the range of 400–600 eV inside the ionization chamber. Additionally, the PIC simulations predict the development of an electric field close to the exit section of the thruster not observed previously because of the practical limitations of experiments. The imbalance of electric charge in the region where the electrons are injected from the only cathode creates a positive field that further accelerates the electric charges, preventing low energy ions from the plasma stream from returning to the plasma thruster.