Recently, the newly-emerging lead-halide perovskite materials have received extensive attention in optoelectronic devices due to their high photoluminescence quantum yield (PLQY), high color purity, and tunable bandgap, etc. However, the toxicity of heavy metal lead seriously hinders their large-scale production and commercialization. Therefore, the development of lead-free perovskite materials with low toxicity has become an urgent research direction in this field. In this work, a lead-free copper-based Rb2CuBr3 material is synthesized by hot-injection method. The effects of Rb+/Cu+ molar ratio and reaction time on the purity and crystallinity of Rb2CuBr3 are investigated. Transmission electron microscopy show that the microstructure of Rb2CuBr3 is a one-dimensional rod-like morphology, which is consistent with their intrinsic one-dimensional crystal structure. Moreover, the as-synthesized Rb2CuBr3 exhibits a bright violet emission located at 390 nm, and a high PLQY of 9175% is obtained. Furthermore, the temperature-dependent photoluminescence (PL) and time-resolved PL decay measurements confirm that the large Stokes shift and broad emission spectra originate from the self-trapped excitons-related radiative recombination. These results indicate that the lead-free Rb2CuBr3 material with high-efficiency luminescence has great application potential in lighting and display fields in the future.