Metric learning has attracted significant attentions in the past decades, for the appealing advances in various realworld applications such as person re-identification and face recognition. Traditional supervised metric learning attempts to seek a discriminative metric, which could minimize the pairwise distance of within-class data samples, while maximizing the pairwise distance of data samples from various classes. However, it is still a challenge to build a robust and discriminative metric, especially for corrupted data in the real-world application. In this paper, we propose a Robust Discriminative Metric Learning algorithm (RDML) via fast low-rank representation and denoising strategy. To be specific, the metric learning problem is guided by a discriminative regularization by incorporating the pair-wise or class-wise information. Moreover, low-rank basis learning is jointly optimized with the metric to better uncover the global data structure and remove noise. Furthermore, fast low-rank representation is implemented to mitigate the computational burden and make sure the scalability on large-scale datasets. Finally, we evaluate our learned metric on several challenging tasks, e.g., face recognition/verification, object recognition, and image clustering. The experimental results verify the effectiveness of the proposed algorithm by comparing to many metric learning algorithms, even deep learning ones.