A one-dimensional electrostatic particle simulation of plasma streaming perpendicular to a magnetic field with nonperiodic boundary condition has been carried out. When a bulk of plasma is injected across an ambient magnetic field, a stream of neutral plasma, consisting of equal numbers of ions and electrons, polarizes, and the resulting polarization electric field gives rise to the penetration of plasma across the magnetic field so that the integrity of plasma maintains. Computer simulation demonstrates the properties of cross-field propagation of plasma stream in a magnetic field with different plasma parameters.