Semi-supervised learning and continuous learning are fundamental paradigms for human-level intelligence. To deal with real-world problems where labels are rarely given and the opportunity to access the same data is limited, it is necessary to apply these two paradigms in a joined fashion. In this paper, we propose Label Propagation Adaptive Resonance Theory (LPART) for semi-supervised continuous learning. LPART uses an online label propagation mechanism to perform classification and gradually improves its accuracy as the observed data accumulates. We evaluated the proposed model on visual (MNIST, SVHN, CIFAR-10) and audio (NSynth) datasets by adjusting the ratio of the labeled and unlabeled data. The accuracies are much higher when both labeled and unlabeled data are used, demonstrating the significant advantage of LPART in environments where the data labels are scarce.