Time series classification is a popular and important topic in machine learning, and it suffers from the class imbalance problem in many real-world applications. In this paper, to address the class imbalance problem, we propose a novel and practical oversampling method named T-SMOTE, which can make full use of the temporal information of time-series data. In particular, for each sample of minority class, T-SMOTE generates multiple samples that are close to class border. Then, based on those samples near class border, T-SMOTE synthesizes more samples. Finally, a weighted sampling method is called on both generated samples near class border and synthetic samples. Extensive experiments on a diverse set of both univariate and multivariate time-series datasets demonstrate that T-SMOTE consistently outperforms the current state-of-the-art methods on imbalanced time series classification. More encouragingly, our empirical evaluations show that T-SMOTE performs better in the scenario of early prediction, an important application scenario in industry, which indicates that T-SMOTE could bring benefits in practice.