Recently, two-dimensional (2D) metal halides have triggered an enormous interest for their tunable mechanical, electronic, magnetic, and topological properties, greatly enriching the family of 2D materials. Here, based on first-principles calculations, we report a systematic study of group 11 transition-metal halide MX (M = Cu, Ag, Au; X = Cl, Br, I) monolayers. Among them, CuBr, CuI, AgBr, and AgI monolayers exhibit high thermodynamic, dynamic, and mechanic stability. The four stable monolayers have a direct band gap of ∼3.12-3.36 eV and possess high carrier mobility (∼103 cm2 V-1 s-1), suggestive of future photocatalysts for water splitting applications. What is more, the simulations of optical properties confirm that the stable MX monolayers hold the potential for further applications in ultraviolet optical devices and quantum cutting solar materials.