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In this paper, we investigate a challenging but interesting task in the research of speech emotion recognition (SER), i.e., cross-corpus SER. Unlike the conventional SER, the training (source) and testing (target) samples in cross-corpus SER come from different speech corpora, which results in a feature distribution mismatch between them. Hence, the performance of most existing SER methods may sharply decrease. To cope with this problem, we propose a simple yet effective deep transfer learning method called progressive distribution adapted neural networks (PDAN). PDAN employs convolutional neural networks (CNN) as the backbone and the speech spectrum as the inputs to achieve an end-to-end learning framework. More importantly, its basic idea for solving cross-corpus SER is very straightforward, i.e., enhancing the backbone's corpus invariant feature learning ability by incorporating a progressive distribution adapted regularization term into the original loss function to guide the network training. To evaluate the proposed PDAN, extensive cross-corpus SER experiments on speech emotion corpora including EmoDB, eNTERFACE, and CASIA are conducted. Experimental results showed that the proposed PDAN outperforms most well-performing deep and subspace transfer learning methods in dealing with the cross-corpus SER tasks.