By using the moving atom-field interaction model, the effects of the atomic motion and the linear change of coupling coefficient on quantum correlations are investigated when the two atoms are in the entangled states and the light field is in the vacuum state. The results show that, as for the single-photon process, the quantum correlations increase with the increment of the structure parameters of field mode. The linear change of coupling coefficient plays a positive role on the quantum correlations. As for the two-photon process, the positive effects of the structure parameters of field mode and the linear change of coupling coefficient on the quantum correlations are more obvious if compared with the case that the coupling coefficient is constant.