In a semimetal, both electrons and holes contribute to the density of states at the Fermi level. The small band overlaps and multiband effects engender novel electronic properties. We show that a moderate hydrostatic pressure effectively suppresses the band gap in the elemental semiconductor black phosphorus. An electronic topological transition takes place at approximately 1.2 GPa, above which black phosphorus evolves into a semimetal state that is characterized by a colossal positive magnetoresistance and a nonlinear field dependence of Hall resistivity. The Shubnikov-de Haas oscillations detected in magnetic field reveal the complex Fermi surface topology of the semimetallic phase. In particular, we find a nontrivial Berry phase in one Fermi surface that emerges in the semimetal state, as evidence of a Dirac-like dispersion. The observed semimetallic behavior greatly enriches the material property of black phosphorus and sets the stage for the exploration of novel electronic states in this material.