The task of aspect-based sentiment analysis aims to identify sentiment polarities of given aspects in a sentence. Recent advances have demonstrated the advantage of incorporating the syntactic dependency structure with graph convolutional networks (GCNs). However, their performance of these GCN-based methods largely depends on the dependency parsers, which would produce diverse parsing results for a sentence. In this article, we propose a dual GCN (DualGCN) that jointly considers the syntax structures and semantic correlations. Our DualGCN model mainly comprises four modules: 1) SynGCN: instead of explicitly encoding syntactic structure, the SynGCN module uses the dependency probability matrix as a graph structure to implicitly integrate the syntactic information; 2) SemGCN: we design the SemGCN module with multihead attention to enhance the performance of the syntactic structure with the semantic information; 3) Regularizers: we propose orthogonal and differential regularizers to precisely capture semantic correlations between words by constraining attention scores in the SemGCN module; and 4) Mutual BiAffine: we use the BiAffine module to bridge relevant information between the SynGCN and SemGCN modules. Extensive experiments are conducted compared with up-to-date pretrained language encoders on two groups of datasets, one including Restaurant14, Laptop14, and Twitter and the other including Restaurant15 and Restaurant16. The experimental results demonstrate that the parsing results of various dependency parsers affect their performance of the GCN-based models. Our DualGCN model achieves superior performance compared with the state-of-the-art approaches. The source code and preprocessed datasets are provided and publicly available on GitHub (see https://github.com/CCChenhao997/DualGCN-ABSA).