Abstract: The interaction between the plutonium atom and hydrogen molecule was calculated and analyzed by using the density functional theory (DFT) and the relativistic effective core potential (RECP) with Gaussian09 program. Due to the special electronic structure of the plutonium atom, it is possible to have multiplet cross in the reaction pathway, so the multiplets of the plutonium atom were considered in calculation. The detailed microscopic reaction process of plutonium atom and hydrogen molecule was calculated as Pu+H₂→FC→TS→PuH₂. The whole reaction process was carried out in the septet state. That is, the reactants, the initial complex, the transition state and the final reaction product in the reaction process are all in septet state. The special structure of the energy minimum points and transition states along the reaction pathway was optimized, and the potential energy profile for energy analysis was drawn. The results of the study are helpful to understand the microscopic reaction process of plutonium atom and hydrogen molecule.