The squeezing properties of a light-atom interacting system are studied by means of quantum theory. In the system,two two-level atoms are initially in an entangled state,and the coherent optical field is in a Schrodinger cat state. Influence of the strength of optical field and the phase angle of the coherent states on the double atoms dipole squeezing and the optical field amplitude squeezing are discussed by numerical calculations. It is found that under weak optical field condition,the optical field amplitude squeezing of even coherent state and Yurke-Stoler coherent state interacting with entangled state of atoms is no existence,but the optical field amplitude squeezing of odd coherent states is existence. In the same condition,the double atomic dipole squeezing of even coherent states interacting with entangled state of atoms is no existence,but the double atomic dipole squeezing of odd coherent state and Yurke-Stoler coherent state is existence. Under strong optical field condition,two squeezing phenomenon is no existence.