The state function of the two-mode SU(1,1) coherent states field interacting with four-level atom added Kerr-like medium was derived. By using the state function it was studied that the influence of the Kerr effect and the initial light field intensity on the two-mode intensity correlation function, the Cauchy-Schwartz inequality, and the second-order correlation function for each mode. The results indicate that the influences of Kerr effects on the properties of the correlation on the correlation intensity between the two-mode on the bunching or antibunching effect of the two-mode SU(1,1) coherent states are obviously related to the initial intensity of the light field.