The entanglement dynamics of the multipartite open system is investigated, which is arranged in such a way that two atoms are coupled to a common non-Markovian reservoir and another two atoms are embedded in the other remote non-Markovian reservoir. The results show that the initial entanglement of two atoms can transfer to another two separated atoms, the two reservoirs have an intermediate effects in the transfer process. Through studying the pairwise concurrence entanglement in the multipartite open system, it is also found that the initial entanglement can cause the phenomenon of entanglement sudden death under certain condition, and the simultaneous entanglement sudden birth would appear in another separated atoms and the two reservoirs.