Distance metric learning has attracted much attention in recent years, where the goal is to learn a distance metric based on user feedback. Conventional approaches to metric learning mainly focus on learning the Mahalanobis distance metric on data attributes. Recent research on metric learning has been extended to sequential data, where we only have structural information in the sequences, but no attribute is available. However, real-world applications often involve attributed sequence data (e.g., clickstreams), where each instance consists of not only a set of attributes (e.g., user session context) but also a sequence of categorical items (e.g., user actions). In this paper, we study the problem of metric learning on attributed sequences. Unlike previous work on metric learning, we now need to go beyond the Mahalanobis distance metric in the attribute feature space while also incorporating the structural information in sequences. We propose a deep learning framework, called MLAS (Metric Learning on Attributed Sequences), to learn a distance metric that effectively measures dissimilarities between attributed sequences. Empirical results on real-world datasets demonstrate that the proposed MLAS framework significantly improves the performance of metric learning compared to state-of-the-art methods on attributed sequences.