Online machine learning is an effective way for observation-based learning when a static dataset is not available. However, it can be challenging in real-world applications, especially when there are missing labels in multi-class classification tasks. Although partial feedback can be applied to tackle the problem, it can make the learning process slow and limit the classification performance as the correct label information is missing when the instance is misclassified. To cope with the lack of the target domain knowledge in online learning, transfer learning can be applied to convey knowledge from one or multiple source domains to the target domain. To this end, we propose a partial feedback online transfer learning algorithm with multiple source domains (PFMSD) to transfer the knowledge learned from multi-source domains to the target domain and enhance the learning performance by exploring the correct label when there is an erroneous prediction. A mistake bound is derived for the proposed algorithm, and extensive experiments are conducted using several wildly-used benchmark datasets. The obtained results in all experiments show the superiority of the proposed algorithm over the state-of-the-art partial feedback algorithms.