Supervised dimensionality reduction for sequence data projects the observations in sequences onto a low-dimensional subspace to better separate different sequence classes. It is typically more challenging than conventional dimensionality reduction for static data, because measuring the separability of sequences involves non-linear procedures to manipulate the temporal structures. This paper presents a linear method, namely Order-preserving Wasserstein Discriminant Analysis (OWDA), which learns the projection by maximizing the inter-class distance and minimizing the intra-class scatter. For each class, OWDA extracts the order-preserving Wasserstein barycenter and constructs the intra-class scatter as the dispersion of the training sequences around the barycenter. The inter-class distance is measured as the order-preserving Wasserstein distance between the corresponding barycenters. OWDA is able to concentrate on the distinctive differences among classes by lifting the geometric relations with temporal constraints. Experiments show that OWDA achieves competitive results on three 3D action recognition datasets.