The energy spectrum and second-order coherence degree of a cascade three-level atom interacting with a single mode binomial state field are calculated accurately in the non-rotating wave approximation. The level-crossing problem is discussed by using fidelity. The influences of the binomial state field parameter η and superposition of atomic energy levels at the initial time on the second-order coherence degree are studied. Results indicate that the duration of the bunching effect decreases gradually with the increase of light field parameter η. The duration of the light field antibunching effect decreases due to the superposition of atomic energy levels. Whether the atom is in superposition state or not at the beginning time, the light field displays antibunching effect completely when the value of η is big enough. Because of the virtual photon effect induced by non-rotating wave approximation, the little indentation oscillation appears in the second-order coherence degree evolution curves.