In realistic settings, a speaker recognition system needs to identify a speaker given a short utterance, while the utterance used to enroll may be relatively long. However, existing speaker recognition models perform poorly with such short utterances. To solve this problem, we introduce a meta-learning scheme with imbalance length pairs. Specifically, we use a prototypical network and train it with a support set of long utterances and a query set of short utterances. However, since optimizing for only the classes in the given episode is not sufficient to learn discriminative embeddings for other classes in the entire dataset, we additionally classify both support set and query set against the entire classes in the training set to learn a well-discriminated embedding space. By combining these two learning schemes, our model outperforms existing state-of-the-art speaker verification models learned in a standard supervised learning framework on short utterance (1-2 seconds) on VoxCeleb dataset. We also validate our proposed model for unseen speaker identification, on which it also achieves significant gain over existing approaches.