Aspect category sentiment analysis (ACSA) aims to predict the sentiment polarities of the aspect categories discussed in sentences. Since a sentence usually discusses one or more aspect categories and expresses different sentiments toward them, various attention-based methods have been developed to allocate the appropriate sentiment words for the given aspect category and obtain promising results. However, most of these methods directly use the given aspect category to find the aspect category-related sentiment words, which may cause mismatching between the sentiment words and the aspect categories when an unrelated sentiment word is semantically meaningful for the given aspect category. To mitigate this problem, we propose a Sentence Constituent-Aware Network (SCAN) for aspect-category sentiment analysis. SCAN contains two graph attention modules and an interactive loss function. The graph attention modules generate representations of the nodes in sentence constituency parse trees for the aspect category detection (ACD) task and the ACSA task, respectively. ACD aims to detect aspect categories discussed in sentences and is a auxiliary task. For a given aspect category, the interactive loss function helps the ACD task to find the nodes which can predict the aspect category but can't predict other aspect categories. The sentiment words in the nodes then are used to predict the sentiment polarity of the aspect category by the ACSA task. The experimental results on five public datasets demonstrate the effectiveness of SCAN.