The lattice constants, cohesive energy, mechanical property and electronic structure of δ-Pu at ground state and high pressure are calculated by a plane wave pseudo-potential method within the framework of density function theory. It shows that δ-Pu is unstable under high pressure and the phase transition happens at about 10GPa, besides, its structural stability decreases with the increase of pressure. The calculated electronic structures indicate that the bonding abilities of 5f and 6d electrons enhance, while the sp hybridization weakens with the increase of pressure. The change of bonding effect caused by the increase of pressure reveals the electronic mechanism of pressure-induced phase transition of δ-Pu.