In this paper, low pressure hydrogen discharges in a transverse magnetic field driven by RF source were addressed theoretically. A one dimensional in position and three dimensional in velocity space Particle-In-Cell plus Monte Carlo Collision model was employed to simulate the hydrogen discharge. The basic properties of such discharge (such as plasma temperature and density, and electron energy distribution function) versus the magnetic field strength were discussed in depth. The simulation results showed that there were marked differences in the discharges between without and with applied magnetic field. The magnetic field with an appropriate strength could enhance both the electron density and energy remarkably. It was also found that a weak magnetic field (weaker than approximately 20 G) could reduce the electron energy but maintain relatively high electron density. (C) 2011 Elsevier B. V. All rights reserved.