Long nanowires of degenerate semiconductor InSb in asbestos matrix (wire diameter about 50 Å, length 0.1-1 mm) have been prepared. The electrical conduction of these nanowires has been studied over a temperature range 1.5-350 K. The zero-field electrical conductance is a power function of temperature G∝T^α with a typical exponent α≈4. Current-voltage characteristics of such nanowires are nonlinear and, at sufficiently low temperatures, follow the power law I∝V^β. The electrical conduction of the nanowires cannot be accounted for in terms of ordinary single-electron theories and exhibits features expected for impure Luttinger liquid (LL). For the simple approximation of an impure LL as a pure liquid broken into drops by weak links, the estimated weak-link density is around 10³-10⁴ cm^-1.