Temporal alignment based k-nearest neighbor classifier is a benchmark for time series classification. Since complex time series generally exhibit different global behaviors within classes in real applications, it is difficult for standard alignment, where features are treated equally while local discriminative behaviors are ignored, to handle these challenging time series correctly and efficiently. To facilitate aligning and classifying such complex time series, this paper proposes a discriminative locally weighted dynamic time warping dissimilarity measure that reveals the commonly shared subsequence within classes as well as the most differential subsequence between classes. Meanwhile, time series alignments of positive and negative subsets are employed to learning discriminative weight for each feature of each time series iteratively. Experiments performed on synthetic and real datasets demonstrate that this locally weighted, temporal alignment based k-nearest neighbor classifier is effective in differentiating time series with good interpretability. Extension of the proposed weighting strategy to multivariate time series is also discussed.