The squeezing properties of the Schr?dinger cat states field interacting with Bose-Einstein condensate of two-level atom are studied by means of quantum theory. The results show that the optical field and the atomic laser of even coherent state and odd coherent state interacting with Bose-Einstein condensate appear no squeezing effects, whereas the optical fields and the atomic laser of Yurke-Stoler coherent state show squeezing effects. The intensity of the initial light field and values of the coupling constant have the influences on the squeezing properties of the field and atomic laser.