In order to better comprehend the dynamic behaviours of ion and electron during the Penning source discharge process under a low pressure and weak ionization condition, numerical simulation is carried out to study the penning source discharge and diffuse process. For constituting 2D axial symmetrical model and combining the particle simulation and Monte Carlo (PIC/MCC) method, elastic collision, excitation, and ionization reactions between electrons and hydrogen molecules, hydrogen atom and ions are taken into account. The effect of magnetic field configuration, secondary electron emission coefficient, derivational voltage, and gas pressure on the discharge characteristics is investigated. It has been found that the simulant discharge parameters, including electron and ion densities, anodic current and ionic current, H+ and H2+ densities, etc, are in good agreement with the experimental results. Based on our numerical simulation, the study of the hydrogen penning discharge is being changed from qualitative analysis to quantitative calculation, which is important for the design and optimization of the penning ion source.