Considering a double JC model with different coupling constants, we investigate the entanglement between the two two-level atoms, and discuss dependence of the atom-atom entanglement on the different coupling constants, and the detuning between the atomic transition frequency and the cavity field frequency. The results show when Δ=δ/g is small, with the increase of the relative difference of the two atom-cavity coupling constants γ, the atom-atom entanglement periodically evolves with the amplitude slowly and periodically modulated. What’s more interesting is that long-lived entanglement between the two atoms can be obtained when atom A non-resonantly interacts with the cavity field a, and atom B has no coupling with the cavity field b. In this case, the concurrence CAB(t) of the two atoms evolves in form of cosine, and is invariant and equals the initial value when far off resonance. In addition, we find that the so-called entanglement sudden death can occur under appropriate conditions on the detunings and the different coupling constants for different initial atomic states.