Motivated by recent experimental observation of an hydrostatic pressure induced transition from semiconductor to semimetal in black phosphorus [Chen et al. in arXiv:1504.00125], we present the first principles calculation on the pressure effect of the electronic structures of black phosphorus. It is found that the band crossover and reversal at the Z point occur around the critical pressure Pc1=1.23 Gpa, and the band inversion evolves into 4 twofold-degenerate Dirac cones around the Z point, suggesting a 3D Dirac semimetal. With further increasing pressure the Dirac cones in the Gamma-Z line move toward the Gamma point and evolve into two hole-type Fermi pockets, and those in the Z-M lines move toward the M point and evolve into 2 hole-type Fermi pockets up to P=4.0 Gpa. It demonstrates clearly that the Lifshitz transition occurs at $P_{c1}$ from semiconductor to 3D Dirac semimetal protected by the nonsymmorphic space symmetry of bulk. This suggests the bright perspective of black phosphorus for optoelectronic and electronic devices due to its easy modulation by pressure.
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