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.
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