The transport properties of hydrogen are crucial to the kinetics of hydrogen storage in MgH2. We use first principle calculations to identify the hydrogen diffusion paths and barriers and diffusion rates in three different MgH2 structures: equilibrium rutile, rutile with ball-milling-induced deformation twins and fluorite polymorph. Hydrogen vacancy mediated mechanism was applied when hydrogen diffusion was studied. We observed that both hydrogen diffusion barriers in deformation twins and fluorite structure are lower compared to that in the equilibrium rutile. This is because the hydrogen diffusion is facilitated by new interstitial sites in the Mg lattice: a new hexahedral site formed by the reconstruction of Mg lattice at the twinning interface in the deformation twins and the octahedral sites in the fluorite structure. Furthermore, the hydrogen vacancy density effect on the diffusion barrier was estimated. The general trend is the higher the density of hydrogen vacancies, the lower the hydrogen diffusion barrier, the higher the diffusion rate. Our results demonstrate how the hydrogen kinetics is altered by controlling the structure of the hydrides.