The quantum entanglement of three-level atoms, which include a V-type three-level atom, a V-type three-level atom and a Λ-type three-level atom, interacting with two-mode SU(1,1) coherent states in a high Q cavity with Kerr medium is studied. By numerical method, the influences of field parameters and Kerr effect on the quantum entanglement are discussed in detail. The result shows the laws of the three type atoms are coincident with the effect of Kerr in a high Q cavity with Kerr medium, before Kerr parameter reaches a certain value the quantum entanglement increases rapidly. However, the quantum entanglement is reduced when the parameter is over the certain value.