Equilibrium geometries, relative stabilities, electronic stabilities and magnetic properties of Co[Formula: see text]Sn ([Formula: see text] = 1–12) clusters have been systematically investigated by using relativistic all-electron density functional theory with generalized gradient approximation. The results indicated that the lowest-energy structures of Co[Formula: see text]Sn ([Formula: see text] = 1–5, 7, 9 and 10) clusters are similar to those of corresponding Co[Formula: see text] clusters. As for Co6Sn, Co8Sn, Co[Formula: see text]Sn and Co[Formula: see text]Sn clusters, the most stable structures give rise to a geometry reconstruction. In the low-lying structures of Co[Formula: see text]Sn ([Formula: see text] = 1–12) clusters, tin impurity prefers to occupy the external site. The second-order difference energy of the ground-state Co[Formula: see text]Sn ([Formula: see text] = 1–12) clusters shows a pronounced odd–even oscillation with the number of Co atoms, and the clusters exhibit higher stability at [Formula: see text] = 5. Compared with corresponding pure Co[Formula: see text] clusters, the total magnetic moment of the Co[Formula: see text]Sn clusters reduces with 1, 3 and 5 [Formula: see text], respectively. The different magnetic changes of the tin doped Co clusters are analyzed in detail based on the magnetism coupling, density of state and hybridization between cobalt and tin atoms.