Several rare-earth monopnictides were shown to exhibit extreme magnetoresistance and field-induced low-temperature plateau of electrical resistivity. These features are also hallmarks of topological semimetals, thus the family is intensively explored with respect to magneto-transport properties and possible hosting Dirac fermion states. We report a comprehensive investigation of Fermi surface and electrical transport properties of LuSb, another representative of this family. At low temperatures, the magnetoresistance of LuSb was found to exceed 3000% without saturation in fields up to 9 T. Analysis of the Hall effect and the Shubnikov-de Haas oscillations revealed that the Fermi surface of this compound consists of several pockets originating from fairly compensated multi-band electronic structure, in full accordance with our first-principles calculations. Observed magnetotransport properties of LuSb can be attributed to the topology of three-dimensional Fermi surface and a compensation of electron and hole contributions.