Aspect-category sentiment analysis (ACSA) aims to identify all the aspect categories mentioned in the text and their corresponding sentiment polarities. Some joint models have been proposed to address this task. However, these joint models do not solve the following two problems well: mismatching between the aspect categories and the sentiment words, and data deficiency of some aspect categories. To solve them, we propose a novel joint model which contains a contextualized aspect embedding layer and a shared sentiment prediction layer. The contextualized aspect embedding layer extracts the aspect category related information, which is used to generate aspect-specific representations for sentiment classification like traditional context-independent aspect embedding (CIAE) and is therefore called contextualized aspect embedding (CAE). The CAE can mitigate the mismatching problem because it is semantically more related to sentiment words than CIAE. The shared sentiment prediction layer transfers sentiment knowledge between aspect categories and alleviates the problem caused by data deficiency. Experiments conducted on SemEval 2016 Datasets show that our proposed model achieves state-of-the-art performance.