By considering a double Jaynes-Cummings (JC) model with linear modulation of the atom-field coupling coefficients, we investigate the entanglement evolution between two atoms, and focuss on the effect of the linear sweep on the entanglement. The results show that the entanglement is very sensitive to the linear modulation of the atom-field coupling coefficients. Both for onephoton processes and for two-photon processes, the disappearance of the initial entanglement is delayed due to the linear modulation as compared to the double standard JC model, and the delayed time is long or short depending on the value of the parameters in the modulation function. Moreover, the entanglement of the two atoms in the double standard JC model disappears periodically. However, this periodicity is completely lost in the linear modulation case. In addition, the larger the photon numbers in the cavities, the shorter the delayed time of the disappearance of the initial entanglement.