Two-dimensional (2D) materials have attracted great interest in the field of optoelectronics in recent years due to their atomically thin structure and various electronic properties. Based on the first-principles calculations combined with the non-equilibrium Green's function (NEGF) method, we predict a set of new 2D ternary materials, sodium copper chalcogenides (NaCuX, X = S, Se, and Te). These materials not only have direct band gaps ranging from 1.2 to 1.6 eV, but also possess relatively small carrier effective masses (0.1-0.2m0) at the band edges thus high carrier mobilities (103-104 cm2 V-1 s-1), which collectively imply that they are suitable for optical-electronic applications in the visible (even in the infrared) light region. Moreover, based on the high photo responsivity (Rph), e.g., up to 0.105 A W-1 for NaCuTe, we design a series of NaCuX monolayer based high performance optoelectronic junctions. These properties indicate that NaCuX monolayers are promising candidate materials for photodetectors and photovoltaic units.