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Materials with high carrier mobility showing large magnetoresistance (MR)have recently received much attention because of potential applications infuture high-performance magneto-electric devices. Here, we report on thediscovery of an electron-hole-compensated half-Heusler semimetal LuPtBi thatexhibits an extremely high electron mobility of up to 79000 cm2/Vs with anon-saturating positive MR as large as 3200% at 2 K. Remarkably, the mobilityat 300 K is found to exceed 10500 cm2/Vs, which is among the highest valuesreported in three-dimensional bulk materials thus far. The clean Shubnikov-deHaas quantum oscillation observed at low temperatures and the first-principlescalculations together indicate that the high electron mobility is due to arather small effective carrier mass caused by the distinctive band structure ofthe crystal. Our finding provide a new approach for finding large,high-mobility MR materials by designing an appropriate Fermi surface topologystarting from simple electron-hole-compensated semimetals.

High Electron Mobility and Large Magnetoresistance in the Half-Heusler Semimetal LuPtBi