The influences of light-field distribution parameters, atomic relative detuning, maximum photon number, light-field probability parameters, and initial atomic states on quantum entanglement characteristics of a system comprising a Pólya-state light field interacting with a Λ-type three-level atom are analyzed based on the quantum entropy theory. The results denote that when the Λ-type three-level atom interacts with the Pólya-state light field and the initial state is a two-lower-level energy-equal superposition state, a stable and periodically oscillating entangled state with a relatively small maximum entanglement degree can be obtained for appropriate parameter values. However, if the initial state is an excited state or a three-level equal-weight superposition state, a stable and periodically oscillating entangled state with a maximum entanglement degree of 1.1 can be obtained for appropriate parameter values.