Process monitoring and fault diagnosis (PM-FD) has been an active research field since it plays important roles in many industrial applications. In this paper, we present a novel data-driven fault diagnosis algorithm which is based on the multivariate dynamic time warping measure. First of all, we propose a Mahalanobis distance based dynamic time warping measure which can compute the similarity of multivariate time series (MTS) efficiently and accurately. Then, a PM-FD framework which consists of data preprocessing, metric learning, MTS pieces building, and MTS classification is presented. After that, we conduct experiments on industrial benchmark of Tennessee Eastman (TE) process. The experimental results demonstrate the improved performance of the proposed algorithm when compared with other classical PM-FD classical methods.