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The key challenge of zero-shot learning (ZSL) is how to infer the latent semantic knowledge between visual and attribute features on seen classes, and thus achieving a desirable knowledge transfer to unseen classes. Prior works either simply align the global features of an image with its associated class semantic vector or utilize unidirectional attention to learn the limited latent semantic representations, which could not effectively discover the intrinsic semantic knowledge e.g., attribute semantics) between visual and attribute features. To solve the above dilemma, we propose a Mutually Semantic Distillation Network (MSDN), which progressively distills the intrinsic semantic representations between visual and attribute features for ZSL. MSDN incorporates an attribute$\rightarrow$visual attention sub-net that learns attribute-based visual features, and a visual$\rightarrow$attribute attention sub-net that learns visual-based attribute features. By further introducing a semantic distillation loss, the two mutual attention sub-nets are capable of learning collaboratively and teaching each other throughout the training process. The proposed MSDN yields significant improvements over the strong baselines, leading to new state-of-the-art performances on three popular challenging benchmarks, i.e., CUB, SUN, and AWA2. Our codes have been available at: \url{https://github.com/shiming-chen/MSDN}.