In practical situations, the emotional speech utterances are often collected from different devices and conditions, which will obviously affect the recognition performance. To address this issue, in this paper, a novel transfer non-negative matrix factorization (TNMF) method is presented for cross-corpus speech emotion recognition. First, the NMF algorithm is adopted to learn a latent common feature space for the source and target datasets. Then, the discrepancies between the feature distributions of different corpora are considered, and the maximum mean discrepancy (MMD) algorithm is used for the similarity measurement. Finally, the TNMF approach, which integrates the NMF and MMD algorithms, is proposed. Experiments are carried out on two popular datasets, and the results verify that the TNMF method can significantly outperform the automatic and competitive methods for cross-corpus speech emotion recognition.