FAR-TECH, Inc., has developed a particle-in-cell Monte Carlo code (EBIS-PIC) to model ion motions in an electron beam ion source (EBIS). First, a steady state electron beam is simulated by the PBGUNS code (see http://far-tech.com/pbguns/index.html). Then, the injected primary ions and the ions from the background neutral gas are tracked in the trapping region using Monte Carlo method. Atomic collisions and Coulomb collisions are included in the EBIS-PIC model. The space charge potential is updated by solving the Poisson equation each time step. The preliminary simulation results are presented and compared with BNL electron beam test stand (EBTS) fast trapping experiments.