Quantum entanglement between a binomial field and a cascade three level atom is studied by using quantum entropy theory, and the influences of the initial state parameters of the field and the atom on the quantum entanglement are discussed. The results show that quantum entanglement of all states from the coherent state to number state interacting with a cascade three level atom can be displayed by using the binomial field property. Steady field-atom qutrit entanglement state can be prepared via the appropriate selection of system parameters.