The structural, electronic and magnetic properties of Cun+1 and CunV (n = 1-12) clusters have been investigated by using density functional theory. The growth behaviors reveal that V atom in low-energy CunV isomer favors the most highly coordinated position and changes the geometry of the three-dimensional host clusters. The vibrational spectra are predicted and can be used to identify the ground state. The relative stability and chemical activity of the ground states are analyzed through the binding energy per atom, energy second-order difference and energy gap. It is found that that the stability of CunV (n ≥ 8) is higher than that of Cun+1. The substitution of a V atom for a Cu atom in copper clusters alters the odd-even oscillations of stability and activity of the host clusters. The vertical ionization potential, electron affinity and photoelectron spectrum are calculated and simulated for all of the most stable clusters. Compare with the experimental data, we determine the ground states of pure copper clusters. The magnetism analyses show that the magnetic moments of CunV clusters are mainly localized on the V atom and decease with the increase of cluster size. The magnetic change is closely related to the charge transfer between V and Cu atoms.