This work presents a simple yet effective model for multi-view metric learning, which aims to improve the classification of data with multiple views, e.g., multiple modalities or multiple types of features. The intrinsic correlation, different views describing same set of instances, makes it possible and necessary to jointly learn multiple metrics of different views, accordingly, we propose a multi-view metric learning method based on Fisher discriminant analysis (FDA) and Hilbert-Schmidt Independence Criteria (HSIC), termed as Fisher-HSIC Multi-View Metric Learning (FISH-MML). In our approach, the class separability is enforced in the spirit of FDA within each single view, while the consistence among different views is enhanced based on HSIC. Accordingly, both intra-view class separability and inter-view correlation are well addressed in a unified framework. The learned metrics can improve multi-view classification, and experimental results on real-world datasets demonstrate the effectiveness of the proposed method.