To explain the unusual nonsaturating linear magnetoresistance observed in silver chalcogenides, the quantum scenario has been proposed based on the assumption of gapless linear energy spectrum. Here we show, by first principles calculations, that β-Ag2Te with distorted antifluorite structure is in fact a topological insulator with gapless Dirac-type surface states. The characteristic feature of this new binary topological insulator is the highly anisotropic Dirac cone, in contrast with known examples, such as Bi2Te3 and Bi2Se3. The Fermi velocity varies an order of magnitude by rotating the crystal axis.