We investigate the transport properties of topological insulator (TI) Bi _0.83Sb _0.17 nanowires. Single-crystal nanowire samples with diameters ranging from 75 nm to 1.1 μm are prepared using high frequency liquid phase casting in a glass capillary; cylindrical single crystals with (101 ¯ 1) orientation along the wire axis are produced. Bi _0.83Sb _0.17 is a narrow-gap semiconductor with an energy gap at the L point of the Brillouin zone, Δ E= 21 meV. The resistance of the samples increases with decreasing temperature, but a decrease in resistance is observed at low temperatures. This effect is a clear manifestation of TI properties (i.e., the presence of a highly conducting zone on the TI surface). When the diameter of the nanowire decreases, the energy gap Δ E grows as 1 / d (for diameter d= 1.1 μ m and d= 75 nm Δ E= 21 and 45 meV, respectively), which proves the presence of the quantum size effect in these samples. We investigate the magnetoresistance of Bi _0.83Sb _0.17 nanowires at various magnetic field orientations. Shubnikov-de Haas oscillations are observed in Bi _0.83Sb _0.17 nanowires at T= 1.5 K, demonstrating the existence of high mobility (μ _S= 26 , 700 - - 47 , 000 cm ²V ^{- 1}s ^{- 1}) two-dimensional (2D) carriers in the surface areas of the nanowires, which are nearly perpendicular to the C₃ axis. From the linear dependence of the nanowire conductance on nanowire diameter at T= 4.2 K, the square resistance R_sq of the surface states of the nanowires is obtained (R_sq= 70 Ohm).