Cross-domain sentiment classification has been a hot spot these years, which aims to learn a reliable classifier using labeled data from the source domain and evaluate it on the target domain. In this vein, most approaches utilized domain adaptation that maps data from different domains into a common feature space. To further improve the model performance, several methods targeted to mine domain-specific information were proposed. However, most of them only utilized a limited part of domain-specific information. In this study, we first develop a method of extracting domain-specific words based on the topic information. Then, we propose a Topic Driven Adaptive Network (TDAN) for cross-domain sentiment classification. The network consists of two sub-networks: semantics attention network and domain-specific word attention network, the structures of which are based on transformers. These sub-networks take different forms of input and their outputs are fused as the feature vector. Experiments validate the effectiveness of our TDAN on sentiment classification across domains.