We have investigated the galvanomagnetic properties of topological insulator based on single-crystal Bi0.83Sb0.17 nanowires. The single-crystal nanowire samples in the diameter range 75 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 singlecrystals with (1011) orientation along the wire axis. The samples resistance increases with decreasing temperature, but at low temperatures decrease in the resistance is observed. This effect is a clear manifestation of the presence on the surface of topological insulators highly conductive zone. We have investigated magnetoresistance of Bi0.83Sb0.17 nanowires at various magnetic field orientations. The oscillations of longitudinal magnetoresistance (MR) of 75 and 100-nm Bi0.83Sb0.17 nanowires with two periods ΔB1 and ΔB2 proportional to Φ0 and Φ0/2 were observed, where Φ0 = h/e is the flux quantum. In the range 0 – 60 degrees of inclined angle of magnetic field, the observed angle variation of the periods is in agreement with the theoretical dependence ΔB(θ) = ΔB(0)/cosθ of the flux quantization oscillations. However, the equidistant oscillations of MR exist in transverse magnetic fields under certain rotation angles. The observed effects are discussed.