Based on the non-local van der Waals density functional (vdW-DF)+U scheme, we carry out the ab initio molecular dynamics (AIMD) study of the interaction dynamics for H2 impingement against the stoichiometric PuO2(111), the reduced PuO2(111), and the stoichiometric α-Pu2O3(111) surfaces. The hydrogen molecular physisorption states, which cannot be captured by pure DFT+U method, are obtained by employing the vdW-DF+U scheme. We show that except for the weak physisorption, PuO 2(111) surfaces are so difficult of access that almost all of the H2 molecules will bounce back to the vacuum when their initial kinetic energies are not sufficient. Although the dissociative adsorption of H2 on PuO2(111) surfaces is found to be very exothermic, the collision-induced dissociation barriers of H2 are calculated to be as high as 3.2 eV and 2.0 eV for stoichiometric and reduced PuO2 surfaces, respectively. Unlike PuO2, our AIMD study directly reveals that the hydrogen molecules can penetrate into α-Pu2O3(111) surface and diffuse easily due to the 25% native O vacancies located along the ⟨111⟩ diagonals of α-Pu2O3 matrix. By examining the temperature effect and the internal vibrational excitations of H2, we provide a detailed insight into the interaction dynamics of H2 in α-Pu2O3. The optimum pathways for hydrogen penetration and diffusion, the corresponding energy barriers (1.0 eV and 0.53 eV, respectively) and rate constants are systematically calculated. Overall, our study fairly reveals the different interaction mechanisms between H2 and Pu-oxide surfaces, which have strong implications to the interpretation of experimental observations.