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Motivated by the great success of dynamic time warping (DTW) in time series matching, Gaussian DTW kernel had been developed for support vector machine (SVM)-based time series classification. Counter-examples, however, had been subsequently reported that Gaussian DTW kernel usually cannot outperform Gaussian RBF kernel in the SVM framework. In this paper, by extending the Gaussian RBF kernel, we propose one novel class of Gaussian elastic metric kernel (GEMK), and present two examples of GEMK: Gaussian time warp edit distance (GTWED) kernel and Gaussian edit distance with real penalty (GERP) kernel. Experimental results on UCR time series data sets show that, in terms of classification accuracy, SVM with GEMK is much superior to SVM with Gaussian RBF kernel and Gaussian DTW kernel, and the state-of-the-art similarity measure methods.