The structural stability and magnetism of Ag atomic chains are studied by the firstprinciples calculations. The chain structures, such as the linear, zigzag, ladder and Tstructure which are formed by three linear chains, are studied. The results show that the linear structure is the most unstable geometry with the lowest cohesive energy. The Tstructure is the most stable geometry, showing the largest cohesive energy. The bond lengths in all the atomic chains studied are shorter than that in the bulk, indicating a stronger bonding strength in the atomic chains as compared with the bulk material. Besides, the study on the magnetism of Ag linear chain reveals that the linear structure could exhibit magnetism when the bond length is compressed by as large as 52%, although the equilibrium linear chain is nonmagnetic. By employing the Stoner criteria and the interaction picture of atomic orbitals, the reason for the possible magnetism of Ag linear chain are explained.