Mining time series data has been revived in the last decade due to the increasing availability of time series datasets. This paper presents an online incremental learning algorithm for time series based on the self-organizing incremental neural network (SOINN) and fast dynamic time warping (FastDTW), referred to as OILFTS. The proposed method OILFTS adopts FastDTW distance as the similarity measure, meeting the requirements of most real-time applications. Moreover, OILFTS achieves online and incremental learning of data series which are of equal or unequal length. We test our method with UCR time series datasets, and experimental results show that, from the respect of classification accuracy, the proposed OILFTS is much better than the state-of-the-art similarity measure approaches and widely investigated kernel-based SVMs.