The predefined artificially-balanced training classes in object recognition have limited capability in modeling real-world scenarios where objects are imbalanced-distributed with unknown classes. In this paper, we discuss a promising solution to the Open-set Long-Tailed Recognition (OLTR) task utilizing metric learning. Firstly, we propose a distribution-sensitive loss, which weighs more on the tail classes to decrease the intra-class distance in the feature space. Building upon these concentrated feature clusters, a local-density-based metric is introduced, called Localizing Unfamiliarity Near Acquaintance (LUNA), to measure the novelty of a testing sample. LUNA is flexible with different cluster sizes and is reliable on the cluster boundary by considering neighbors of different properties. Moreover, contrary to most of the existing works that alleviate the open-set detection as a simple binary decision, LUNA is a quantitative measurement with interpretable meanings. Our proposed method exceeds the state-of-the-art algorithm by 4-6% in the closed-set recognition accuracy and 4% in F-measure under the open-set on the public benchmark datasets, including our own newly introduced fine-grained OLTR dataset about marine species (MS-LT), which is the first naturally-distributed OLTR dataset revealing the genuine genetic relationships of the classes.