Single crystals of a small bimetallic Ag3Cu2 nanocluster protected by six ligands of 2,4-dimethylbenzene thiol are synthesized by a one-pot procedure of wet chemistry. This Ag3Cu2 nanocluster bears a trigonal bipyramid metallic core with two copper atoms located on both sides of a triangular Ag3. Interestingly, the six Cu-Ag side edges of the trigonal bipyramid are fully protected by the six ligands giving rise to reinforced stability and high chemical purity. More interestingly, this Ag3Cu2 cluster shows strong dual fluorescence emissions in both ultraviolet visible (UV-vis) and near infrared (NIR) regions. Theoretical calculations reproduce the absorption and fluorescence spectra where the NIR emission at 824 nm is assigned to the S1→ S0 transition, while the simultaneous emission in the visible band is due to the radiation of highly excited states and is against Kasha's rule.