<p>Unsupervised multi-source domain adaptation methods transfer knowledge learned from multiple labeled source domains to an unlabeled target domain. Existing methods assume that all source domain data can be accessed directly. However, such an assumption is unrealistic and causes data privacy concerns, especially when the source domain labels include personal information. In such a setting, it is prohibited to minimize domain gaps by pairwise calculation of the data from the source and target domains. Therefore, this work addresses the source-free unsupervised multi-source domain adaptation problem, where only the source models are available during the adaptation. We propose trust center sample-based source-free domain adaptation (TSDA) method to solve this problem. The key idea is to leverage the pre-trained models from the source domain and progressively train the target model in a self-learning manner. Because target samples with low entropy measured from the pre-trained source model achieve high accuracy, the trust center samples are selected first using the entropy function. Then pseudo labels are assigned for target samples based on a self-supervised pseudo-labeling strategy. For multiple source domains, corresponding target models are learned based on the assigned pseudo labels. Finally, multiple target models are integrated to predict the label for unlabeled target data. Extensive experiment results on some benchmark datasets and generated adversarial samples demonstrate that our approach outperforms existing UMDA methods, even though some methods can always access source data.</p>