In this paper the first-principles calculations within local spin density approximation(LSDA)+U show that BiFeO3 experiences a mixed phase state with P4mm structure being the intermediate phase before the pressure of phase transition is reached.The critical pressure for the insulator-metal transition(IMT)is found to be about 50 GPa.A pressure induced crossover of high-spin states and low-spin states is observed close to the IMT pressure in R3c structure.The LSDA+U calculations account well for the mechanism of the IMT and crossover of spin states predicted in recent experiment(Re[1]).