The quantum properties of a binomial state field interacting with a Λ-type three-level atom are calculated accurately under non-rotating wave approximation. The influences of the binomial state field parameter and the superposition of atomic energy level at the initial time on the second-order coherence degree and the field squeezing effect are discussed. The numerical results indicate that the duration of the anti-bunching effect and the duration of the bunching effect due to the superposition of atomic energy level at the initial time becomes longer, with the increase of binomial state field parameter. Increasing the field parameter, the duration of the squeezing effect increases at first and then decreases whether the atomic energy level has a superposition or not. The little indentation oscillation appears in the evolution curves of the second-order coherence degree and the field squeezing effect, because of the virtual photon effect induced by non-rotating wave approximation.