Time series classification is an important research topic in machine learning and data mining communities, since time series data exist in many application domains. Recent studies have shown that machine learning algorithms could benefit from good feature representation, explaining why deep learning has achieved breakthrough performance in many tasks. In deep learning, the convolutional neural network (CNN) is one of the most well-known approaches, since it incorporates feature learning and classification task in a unified network architecture. Although CNN has been successfully applied to image and text domains, it is still a challenge to apply CNN to time series data. This paper proposes a tensor scheme along with a novel deep learning architecture called multivariate convolutional neural network (MVCNN) for multivariate time series classification, in which the proposed architecture considers multivariate and lag-feature characteristics. We evaluate our proposed method with the prognostics and health management (PHM) 2015 challenge data, and compare with several algorithms. The experimental results indicate that the proposed method outperforms the other alternatives using the prediction score, which is the evaluation metric used by the PHM Society 2015 data challenge. Besides performance evaluation, we provide detailed analysis about the proposed method.