Sentiment analysis is the process of determining the feeling polarity expressed in human opinions. Various methods have been proposed to improve the performance of sentiment analysis, notably supervised learning methods. However, the performance of sentiment analysis methods when tested depends heavily on the domain of the training dataset. That is, if the domain of the training dataset and the domain of the testing dataset are different, the performance achieved on the testing dataset may not be good. This is a challenge that has not been thoroughly solved so far. In this paper, we propose a multi-domain sentiment analysis method based on the graph convolutional network (GCN) which includes the following main steps: (i) Sentences with different domains are converted into domain-specific vectors using the DomBert model; (ii) The domain-specific vectors are fed into GCN models to extract features and create domain-specific feature vectors; (iii) Domain-specific feature vectors are fed into softmax function-based classifiers to determine sentiment polarity; (iv) Fusion layer is constructed to combine results from data classifiers; (v) The proposed method is trained and its performance is determined. The proposed method is experimented on different domain datasets. The results have demonstrated the contribution of our idea.