The structures and spectra of Cunb (n = 3–16; b = 0, ±1) clusters have been researched by means of density functional theory (DFT) coupled with CALYPSO structure prediction method. It is found that the growth of Cun (n = 9–16) clusters shows a clear regularity. Based on the global minimum structure of the Cun cluster, the UV spectra have been predicted and are in good agreement with the available experimental results. The most stable structures of anionic copper clusters have been identified by comparing experimental and theoretical photoelectron spectra (PES). The infrared (IR) and Raman spectra of cationic copper clusters have been simulated and the calculated IR spectra of Cun+ -Arm (n = 3–10) complexes are in accord with experimental spectra. The Ar atoms adsorbed to small Cun+ cluster have partly influence on the IR spectrum of the host cluster. The Cu6, Cu8 and Cu3+ clusters can be regard as three magic clusters.