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We have used systematic ab initio evolutionary structural searching to uncover the high-pressure transformation pathway of a promising thermoelectric material, AgGaTe2. The global structures of the ternary Ag-Ga-Te system have been predicted up to 100 GPa. The known chalcopyrite phase at ambient pressure is validated by the searching method. The B3-like structure with the space group (s.g.) of P((4) over bar)m(2) exhibits a metastable one at a low-pressure range. The first structural phase transition is calculated at about 4 GPa, processing the I((4) over bar) (2)d phase to a B1-like phase (s.g. Pmma). Other predicted structures, Pmn2(1) and Pm phases, are potentially coexisting phases up to 30 GPa because of the slightly different enthalpy. This finding reasonably explains the ambiguous results in the previous experiments. The high-pressure phase beyond 30 GPa is proposed to be a short-range alloy of bcc-Te and B2-AgGa rather than a cation-disordered B2-like phase. The band gap of the I((4) over bar)(2)d phase is increased with increasing pressure, while the metastable P((4) over bar)(2)m(2) phase is a narrow band gap semiconductor. The electron-phonon coupling of the metallic phases of ternary IB-IIIA-VIA(2) compounds is derived for the first time in AgGaTe2. They exhibit superconductors with a maximum Tc of 2.4 K in the Pmma phase at 6 GPa. The findings of this work not only provide a clear explanation of the high-pressure transformation pathway of AgGaTe2 but also suggest promising electronic properties guiding further applications, especially in a thermometric device, of this material under high pressure.