The squeezing effect and atomic population of the binomial field interacting with a cascade three level atom are calculated accurately without rotatingwave approximation(without RWA) by using the complete quantum theory. The influences of the binomial state field parameter η on the field squeezing effect and the maximum photon number M of the binomial state field on the atomic population are considered. The results obtained from using the numerical method show that with increase of the binomial state field parameter η, the duration of the squeezing effect increases at first and then decreases. The little indentation oscillation appears in the evolution curves of the field squeezing effect, which is caused by virtual photon without RWA. The period of the revivalcollapse increases with the increase of the maximum photon number M, and the atomic population can not collapse completely in the collapse regime, but displays little indentation oscillation. In addition the influence of the withoutRWA terms on the quantum properties of the system are discussed.