Among the group-III chalcogenides, the two-dimensional (2D) GaSe and GaTe materials have been synthesized, but recent theoretical studies have raised controversial results regarding their thermoelectric (TE) properties. Hereby, systematically investigated the temperature and carrier concentration dependent TE properties of 2D GaSe and GaTe. We found that the GaSe had an indirect band gap of 2.94 eV while the GaTe had an indirect band gap of 1.88 eV. Both materials had almost the same Seebeck coefficients, but the p-type GaTe had the longest carrier relaxation time. We obtained the largest electrical conductivity over the thermal conductivity ratio in p-type GaTe compared with all other systems. This results in a very high p-type ZT of 0.91. Moreover, this high ZT performance is only changed by approximately 7% in a wide range of temperatures (300-700 K) and carrier concentration (1011-1013 hole cm-2). Compared with previously reported results, we find that it is necessary to consider the carrier relaxation time and spin-orbit coupling effect for determining reliable TE property. Overall, we propose that the p-type GaTe have outstanding TE property, and it can be utilized for potential TE device applications.