This paper investigates how to learn the distance between multilinear samples. First, for tensor data, we present a new distance metric called as tensorbased Mahalanobis distance. Then the distance is learned through solving a model of tensor-based maximally collapsing metric learning. The proposed metric learning technique has the advantage of few parameters. At the same time, it is also employed to perform dimensionality reduction. Finally, face recognition experiments demonstrate the superiority of the learned distance over the Euclidean distance.