We first derive the state vector of a V-type three-level atom interacting with two-mode SU (1,1) coherent states in a Kerr-like medium. It is shown by numericl calculations that the Kerr effect results indifferent characters of the Rabi oscillation, as compared with the two-levelatom case, while the correlation of the two-mode coherent states is less affected by the the Kerr medium. We also discuss the influence of Kerr effect on the Cauchy-Schwartz inequality.