We propose a scheme for robustly storing multi-atom entangled states involving Bell states, three-particle W-state, n-particle W-like-states, generalized multi-particle W-states, n-particle GHZ-states, and partially entangled states in cavity QED. Our scheme can preserve the internal structure of the entangled states above, with only generation of a global phase corresponding to each of entangled states during the storage of them. One single-mode cavity and n identical two-level atoms are required. Our scheme may be realized in the present technology. The idea may be also utilized to store multi-trapped-ion entangled states in linear ion trap.