Topological insulators, a new quantum state of matter, create exciting opportunities for studying topological quantum physics and for exploring spintronic applications due to their gapless helical metallic surface states. Here, we report the observation of weak anti-localization and quantum oscillations originated from surface states in Bi₂Se₂Te crystals. Angle-resolved photoemission spectroscopy measurements on cleaved Bi₂Se₂Te crystals show a well-defined linear dispersion without intersection of the conduction band. The measured weak anti-localization effect agrees well with the Hikami-Larkin-Nagaoka model and the extracted phase coherent length shows a power-law dependence with temperature (l(Φ)∼T⁻⁰·⁴⁴), indicating the presence of the surface states. More importantly, the analysis of a Landau-level fan diagram of Shubnikov-de Hass oscillations yields a finite Berry phase of ∼0.42π, suggesting the Dirac nature of the surface states. Our results demonstrate that Bi₂Se₂Te can serve as a suitable topological insulator candidate for achieving intrinsic quantum transport of surface Dirac fermions.