Considering a two-level atom interacting with the competing two-mode field, this paper investigates the entangle-ment between the two-level atom and the two-mode field by using the quantum reduced entropy, and that between the two-mode field by using the quantum relative entropy of entanglement. It shows that the two kinds of entanglement are dependent on the relative coupling strength of atom-field and the atomic distribution, and exhibit the periodical evolu-tion. The maximal atom-field entanglement state can be prepared via the appropriate selection of system parameters and interaction time.