By using the field (atom) reduced entropy and quantum relative entropy, the entanglement properties of various two-mode non-classical optical fields(including the entangled coherent state, pair coherent state and two-mode squeezed vacuum state) interacting with a Ξ type three-level atom are investigated. Influences of the atom initial states and field parameters are discussed, and the comparison with Bell operator expectation value constructed by the pseudo spin operator is carried out. Results show that there is similar evolution trend between entropy and Bell operator expectation value. Compared with Bell operator expectation value, entropy is more easily influenced by atom coherence. The nonlocality reaches the maximum when entanglement reaches the maximum, and the expectation value of Bell operator is not the minimum when entanglement reaches the minimum. When the expectation value of Bell operator is less, entanglement is still maybe larger. It shows that the entanglement and nonlocality are two kinds of interconnected and independent properties in quantum world.