We present evidence of topological surface states in β-Ag2Te through first-principles calculations, periodic quantum interference effect and ambipolar electric field effect in single crystalline nanoribbon. Our first-principles calculations show that β-Ag2Te is a topological insulator with a gapless Dirac cone with strong anisotropy. To experimentally probe the topological surface state, we synthesized high quality β-Ag2Te nanoribbons and performed electron transport measurements. The coexistence of pronounced Aharonov-Bohm oscillations and weak Altshuler-Aronov-Spivak oscillations clearly demonstrates coherent electron transport around the perimeter of β-Ag2Te nanoribbon and therefore the existence of topological surface states, which is further supported by the ambipolar electric field effect for devices fabricated by β-Ag2Te nanoribbons. The experimental evidences of topological surface states and the theoretically predicted anisotropic Dirac cone of β-Ag2Te suggest that the material may be a promising candidate of topological insulator for fundamental study and future spintronic devices.