We have investigated the transport properties of topological insulator based on single-crystal Bi0.83Sb0.17 nanowires. The single-crystal nanowire samples in the diameter range 200 nm – 1.1 μm were prepared by the high frequency liquid phase casting in a glass capillary using an improved Ulitovsky technique; they were cylindrical single-crystals with (1011) orientation along the wire axis. In this orientation, the wire axis makes an angle of 19.5o with the bisector axis C1 in the bisector-trigonal plane. Bi0.83Sb0.17 is a narrow gap semiconductor with energy gap at L point of Brillouin zone ΔE= 21 meV. In accordance with the measurements of the temperature dependence of the resistivity of the samples resistance increases with decreasing temperature, but at low temperatures decrease in the resistance is observed. This effect, decrease in the resistance, is a clear manifestation of the interesting properties of topological insulators - the presence on its surface of a highly conducting zone. The Arrhenius plot of R in samples d=1.1 μm and d=200 nm indicates a thermal activation behavior with an activation gap ΔE= 21 and 40 meV, respectively, which proves the presence of the quantum size effect in these samples. We found that in the range of diameter 1100 nm - 200 nm when the diameter decreases the energy gap is growing exponentially. We have investigated magnetoresistance of Bi0.83Sb0.17 nanowires at various magnetic field orientations. From the temperature dependences of Shubnikov de Haas oscillation amplitude for different orientation of magnetic field we have calculated the cyclotron mass mc and Dingle temperature TD for longitudinal and transverse (B||C3 and B||C2) directions of magnetic fields, which equal 1.96*10-2 m0, 9.8 K, 8.5*10-3 m0 , 9.4 K and 1.5*10-1 m0 , 2.8 K respectively. The observed effect are discussed.