The control of the electron temperature and charged particle transport in negative hydrogen ion sources has a crucial role for the performance of the system. It is usually achieved by the use of a magnetic filter—localized transverse magnetic field, which reduces the electron temperature and enhances the negative ion yield. There are several works in literature on modeling of the magnetic filter effects based on fluid and kinetic modeling, which, however, suggest rather different mechanisms responsible for the electron cooling and particle transport through the filter. Here a kinetic modeling of the problem based on the particle-in-cell with Monte Carlo collisions method is presented. The charged particle transport across a magnetic filter is studied in hydrogen plasmas with and without including volume production of negative ions, in a one-dimensional Cartesian geometry. The simulation shows a classical (collisional) electron diffusion across the magnetic filter with reduction in the electron temperature but no selective effect in electron energy is observed (Coulomb collisions are not considered). When a bias voltage is applied, the plasma is split into an upstream electropositive and a downstream electronegative regions. Different configurations with respect to bias voltage and magnetic field strength are examined and discussed. Although the bias voltage allows negative ion extraction, the results show that volume production of negative ions in the downstream region is not really enhanced by the magnetic filter.