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Magnetic topological insulator is an ideal platform to explore the interaction between magnetism and topological orders. As an intrinsic magnetic topological insulator, MnBi₂Te₄ has gained a lot of attention, but its properties are yet to be fully understood. Due to its antiferromagnetic nature below Néel temperature, MnBi₂Te₄ thin film is a quantum anomalous Hall (QAH) insulator at odd layers, while an axion insulator at even layers. Recent experiments have shown that the anomalous Hall measurements in MnBi₂Te₄ films exhibit unique even-odd layer-dependent patterns, which could be linked to its distinct topological states at even and odd layers. Here we theoretically studied the underlying mechanism of this intriguing behavior, and discussed the interplay between the axion electrodynamics and the antiferromagnetism for the even-layer systems. These results may provide a deeper insight of the newly-discovered material MnBi₂Te₄ and the interaction between topology and magnetic orders.