A numerical technique based on Brownian dynamic simulation for the aggregation of charged particles in the free molecular regime is presented. The Langevin equation is used for tracking each particle making up an aggregate. A periodic boundary condition is used for calculation of the aggregation process in each cell with 500 primary particles of 16 nm in diameter. Particle motion is based on the thermal force and the electrostatic force, The electrostatic force on a particle in the simulation cell is considered as a sum of electrostatic forces from other particles in the original cell and its replicate cells. We assume that the electric charges accumulated on an aggregate are located on its center of mass, and aggregates are only charged with pre-charged primary particles. The morphological shape of aggregates is described in terms of the fractal dimension. The fractal dimension for the uncharged aggregate was D-f = 1.761, and changed slightly for the various amounts of bipolar charge. However, in case of unipolar charge, the fractal dimension decreased from 1.641 to 1.537 with the increase of the average number of charges on the particles from 0.2 to 0.3 in initial states. During the early and middle stages of aggregation process, the average aggregate size in the bipolar charge state was larger than in the uncharged state, but was almost equal in the final stage. On the other hand, in the unipolar charge state, the average size of an aggregate and the dispersion of particle volume decreased with increasing charge.