In this paper, the quantum properties of light in a system of two coupling atoms interacting with a single-model squeezed vacuum field at the two-photon transition in Kerr medium are studied by means of quantum theory.The influences of the Kerr medium and the dipole-dipole interaction between atoms are discussed. The results show that when the Kerr effect and the dipole-dipole interaction between atoms may be neglected, the fluctuation of U2 can be squeezed periodically. With increasing the Kerr effect and the dipole-dipole interaction between atoms, the squeezing effect of light gradually becomes weak and the squeezing time of light gradually decreases. The periodical collapse-revival phenomenon of the time evolution of the second-order coherence degree of the field appears, which is caused by the influence of the Kerr effect and the dipole-dipole interaction between atoms. No matter how large are the coupling constants, the photon bunching always appears.