Existing aspect-based/category sentiment analysis methods have shown great success in detecting sentiment polarity toward a given aspect in a sentence with supervised learning, where the training and inference stages share the same pre-defined set of aspects. However, in practice, the aspect categories are changing rather than keeping fixed over time. Dealing with unseen aspect categories is under-explored in existing methods. In this article, we formulate a new few-shot aspect category sentiment analysis (FSACSA) task, which aims to effectively predict the sentiment polarity of previously unseen aspect categories. To this end, we propose a novel Aspect-Focused Meta-Learning (AFML) framework that constructs aspect-aware and aspect-contrastive representations from external knowledge to match the target aspect with aspects in the training set. Concretely, we first construct two auxiliary contrastive sentences for a given sentence with the incorporation of external knowledge, enabling the learning of sentence representations with a better generalization. Then, we devise an aspect-focused induction network to leverage the contextual sentiment toward a given aspect to refine the label vectors. Furthermore, we employ the episode-based meta-learning algorithm to train the whole network, so as to learn to generalize to novel aspects. Extensive experiments on multiple real-life datasets show that our proposed AFML framework achieves the state-of-the-art results for the FSACSA task.