In many real-world applications of the time series classification problem, not only could the negative training instances be missing, the number of positive instances available for learning may also be rather limited. This has motivated the development of new classification algorithms that can learn from a small set P of labeled seed positive instances augmented with a set U of unlabeled instances (i.e. PU learning algorithms). However, existing PU learning algorithms for time series classification have less than satisfactory performance as they are unable to identify the class boundary between positive and negative instances accurately. In this paper, we propose a novel PU learning algorithm LCLC (Learning from Common Local Clusters) for time series classification. LCLC is designed to effectively identify the ground truths’ positive and negative boundaries, resulting in more accurate classifiers than those constructed using existing methods. We have applied LCLC to classify time series data from different application domains; the experimental results demonstrate that LCLC outperforms existing methods significantly.