Imbalanced music genre classification is a crucial task in the Music Information Retrieval (MIR) field for identifying the long-tail, data-poor genre based on the related music audio segments, which is very prevalent in real-world scenarios. Most of the existing models are designed for class-balanced music datasets, resulting in poor performance in accuracy and generalization when identifying the music genres at the tail of the distribution. Inspired by the success of introducing Multi-instance Learning (MIL) in various classification tasks, we propose a novel mechanism named Multi-instance Attention (MATT) to boost the performance for identifying tail classes. Specifically, we first construct the bag-level datasets by generating the album-artist pair bags. Second, we leverage neural networks to encode the music audio segments. Finally, under the guidance of a multi-instance attention mechanism, the neural network-based models could select the most informative genre to match the given music segment. Comprehensive experimental results on a large-scale music genre benchmark dataset with long-tail distribution demonstrate MATT significantly outperforms other state-of-the-art baselines.