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We report the crystal and electronic structures of a noncentrosymmetric quasi-two-dimensional (2D) candidate of topological semimetal AuTe2Br. The Fermi surface of this layered compound consists of 2D-like, topological trivial electron and nontrivial hole pockets, which host a Dirac cone along the kz direction. Our transport measurements on the single crystals show highly anisotropic, compensated low-density electrons and holes, both of which exhibit ultrahigh mobility at a level of 105 cm2 V−1 s−1 at low temperature. The highly mobile, compensated carriers lead a nonsaturated, parabolic magnetoresistance as large as 3 × 105 in single-crystalline AuTe2Br in a magnetic field up to 58 T.