Two-dimensional (2D) topological insulators (TIs) are recently recognized states of quantum matter that are highly interesting for lower-power-consuming electronic devices owing to their nondissipative transport properties protected from backscattering. So far, only few 2D TIs, suffering from small bulk band gap (<10meV), have been experimentally confirmed. Here, through first-principles calculations, we propose a family of 2D TIs in group-11 chalcogenide 2D crystals, M2Te(M=Cu,Ag). The nontrivial topological states in Cu2Te and Ag2Te 2D crystals, identified by topological invariant and edge state calculations, exhibit sizeable bulk gaps of 78 and 150 meV, respectively, suggesting that they are candidates for room-temperature applications. Moreover, strain engineering leads to effective control of the nontrivial gaps of Cu2Te and Ag2Te, and a topological phase transition can be realized in Cu2Te, while the nontrivial phase in Ag2Te is stable against strain. Their dynamic and thermal stabilities are further confirmed by employing phonon calculations and ab initio molecular dynamic simulations.