  Rare-earth monopnictides are predicted to be nontrivial semimetal candidates
and show pressure-induced superconductivity. Here, we grow LuBi single crystal
and study the magnetization, transport behaviors and electronic band structures
to reveal its topological semimetal feature and superconductivity under
pressure. At 0 GPa, the quantum oscillations indicate that there are several
topologically nontrivial carrier pockets around the Fermi level, among which
the hole ones are isotropic in shape, while the electron ones are anisotropic
and responsible for the angular magnetoresistance. Upon compression, the
superconductivity emerges in the titled compound, showing a similar pressure
dependence as that observed in LaBi. Our calculation suggests that the
electronic band structures are robust at low- and high-pressure respectively
and thus the topological features are always preserved. Besides, the nearly
pressure-independent density of state in LuBi indicates that the conventional
electron-phonon coupling appears to play a minor role in the superconductivity.
