In this work, we propose a model to investigate the hydrogen storage ab/desorption kinetic properties for the pure MgH2 using Kinetic Monte Carlo (KMC) simulations. To do such computations, the activation energies for different elementary processes have been estimated. Moreover, the different thermodynamical quantities of interest are determined by performing the ab-initio calculations. Then, we discuss the hydrogen diffusion in magnesium hydride (such as adsorption, diffusion and desorption). More precisely, we study the effect of each elementary mechanism on the diffusion that we characterize through the density distribution of hydrogen atoms including filling ratios, diffusion time, temperature and pressure. Among others, we show that all elementary mechanisms are needed to reproduce a behavior of ab/desorption which correlates well with the experimental results reported in literature. In particular, at high temperature and pressure, the results of simulations indicate that the studied material involves slow kinetics. Copyright (C) 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.