A simulation of the beam-plasma discharge is attempted in this paper by using a particle-in-cell code in a one-dimensional system. Two different boundary conditions are adopted in the present study. When the open boundary condition is used, the stagnation region expands slowly and most ionization occurs only in a limited region near the beam injection boundary. The electrostatic energy deposited from the beam is inversely proportional to the electron-neutral collision frequency. When this open boundary is replaced by a grounded conducting wall, the stagnation point formed initially near the emitter moves quickly toward the wall and significant ionization is observed in the entire system. Beam-plasma instability is observed in the late evolution of the bounded system.