In this work, a novel approach utilizing feature covariance matrices is proposed for time series classification. In order to adapt the feature covariance matrices into time series classification problem, a feature vector is defined for each point in a time series. The feature vector comprises local and global information such as value, derivative, rank, deviation from the mean, the time index of the point and cumulative sum up to the point. Extracted feature vectors for the time instances are concatenated to construct feature matrices for the overlapping subsequences. Covariances of the feature matrices are used to describe the subsequences. Our main purpose in this work is to introduce and evaluate the feature covariance representation for time series classification. Therefore, in classification stage, firstly, 1-NN classifier is utilized. After showing the effectiveness of the representation with 1-NN classifier, the experiments are repeated with SVM classifier. The other novelty in this work is that a novel distance measure is introduced for time series by feature covariance matrix representation. Conducted experiments on UCR time series datasets show that the proposed method mostly outperforms the well-known methods such as DTW, shapelet transform and other state-of-the-art techniques.