In this paper we have investigated the entanglement evolutions between a two-level atom and a single-mode field as well as two two-level atoms in different W-like initial states in T-C model. It is shown that the evolutions of the formation entanglement between them are periodical, and the periods of the entanglement evolutions are different according to the difference of the initial states.The so-called sudden death of entanglement occures between two atoms as the initial states is some W-like initial state.