Few-shot Aspect Category Sentiment Analysis (ACSA) is a crucial task for aspect-based sentiment analysis, which aims to detect sentiment polarity for a given aspect category in a sentence with limited data. However, few-shot learning methods focus on distance metrics between the query and support sets to classify queries, heavily relying on aspect distributions in the embedding space. Thus, they suffer from overlapping distributions of aspect embeddings caused by irrelevant sentiment noise among sentences with multiple sentiment aspects, leading to misclassifications. To solve the above issues, we propose a metric-free method for few-shot ACSA, which models the associated relations among the aspects of support and query sentences by Dual Relations Propagation (DRP), addressing the passive effect of overlapping distributions. Specifically, DRP uses the dual relations (similarity and diversity) among the aspects of support and query sentences to explore intra-cluster commonality and inter-cluster uniqueness for alleviating sentiment noise and enhancing aspect features. Additionally, the dual relations are transformed from support-query to class-query to promote query inference by learning class knowledge. Experiments show that we achieve convincing performance on few-shot ACSA, especially an average improvement of 2.93% accuracy and 2.10% F1 score in the 3-way 1-shot setting.