  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.
