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Abstract Multivariate time series (MTS) classification is a fundamental problem in time series mining, and the approach based on covariance matrix is an attractive way to solve the classification. In this study, it is noted that a traditional covariance matrix is only a particular form of kernel matrices, and then presented a classification method for MTS. First, the Gaussian kernel matrix is employed to replace the traditional covariance matrix. Then the kernel matrix is mapped into the tangent space of Riemannian manifold. Finally, the classification is implemented by choosing a classification algorithm. The experimental results show that the classification performance based on the Gaussian kernel matrix outperforms the other two methods, which indicates that an appropriate kernel function is an essential factor in improving the classification performance.