First-principles calculations were performed to investigate the structure, stability, and electronic properties of two-dimensional noble metal monolayers, including Cu, Ag, and Au, inspired by the recent synthesis of a two-dimensional gold monolayer. All 2D noble metals exhibit great stability with almost standard equilateral triangular lattice structures. These monolayers can survive 10 ps MD annealing simulations under 300 K. Phonon spectra do not exhibit negative frequencies. The independent elastic constants, Young's modulus, and Poisson's ratio were obtained, indicating that these monolayers are mechanically stable and slightly anisotropic. Additionally, the results of band structures and density of states (DOS) calculations reveal typical metallic electronic properties. The dumbbell-like Fermi surfaces suggest anisotropic electron transport properties. These findings highlight the immense application potential of 2D noble metal monolayers in diverse fields.