The geometries, total energies, and frequencies of ZrnCo (n=1—13) clusters have been systematically investigated by using density functional theory with the generalized gradient approximation. The equilibrium geometries, stabilities, gap and magnetism have been determined. The results show that the relative stabilities of Zr4Co, Zr7Co, Zr9Co and Zr12Co are stronger than other sized clusters, indicating that they are magic number clusters, and especially, the true ground state for Zr12Co cluster has icosahedral structure with Ih symmetry. Moreover, the stability of Zr12Co is the strongest of all the investigated clusters. The magnetic moment of ZrnCo clusters mainly comes from the localized d electron. The system magnetic moment may be divided into three stages along with the size change: n=1—3 corresponds to the stable magnetic moment, the magnetic moment of ZrnCo clusters starts to show vibration quenching from n=4, until n=8 when the magnetic moments is completely quenched. The charge transfer and the strong hybridization between s, p and d states might be one major reason for quenching of the magnetic moment of ZrnCo clusters. Meanwhile, the clusters which are composed of transition metals doped in different characteristic materials is worth further studying, for example, TMX12 and Zr13TM clusters have interestingly similar structures, stability and magnetism.