Abstract: The comparative study between the electronic structures of α-Pu and δ-Pu was conducted by a plane wave pseudo-potential method within the framework of density functional theory. It’s learned from the charge population that the 8 kinds of atoms in α-Pu have different charge distributions, and the gain and loss of net charge are mainly contributed by s and p electrons, while the atoms in δ-Pu have the same charge distribution with no gain or loss of net charge. It’s learned from density of states (DOS) that α-Pu has relatively lower and wilder DOS peak than δ-Pu, indicating that the average bond energy of α-Pu is stronger than that of δ-Pu, which results in a more difficult plastic deformation for α-Pu. Besides, the energy of α-Pu electrons is generally lower than that of δ-Pu electrons, which is an important reason for the better stability of α-Pu at room temperature. And it’s learned from partial density of states (PDOS) that, the correlation of 5f electrons of Pu atom at site 8 is the strongest, with the greatest contribution to the spin moment of α-Pu, while at site 1 it is the weakest, with the smallest contribution to the spin moment. It’s learned from the electron density that the atoms in δ-Pu have round electron clouds without obvious interaction, presenting the typical feature of metallic bonds, while the electron clouds of atoms in α-Pu overlap with each other and the bonds are covalent in character, which to some degree reveals the mechanism of different ductility and brittleness of δ-Pu and α-Pu.