Domain adaptive object detection (DAOD) aims to generalize detectors trained on an annotated source domain to an unlabelled target domain. Traditional works focus on aligning visual features between domains to extract domain-invariant knowledge, and recent VLM-based DAOD methods leverage semantic information provided by the textual encoder to supplement domain-specific features for each domain.However, they overlook the role of semantic information in guiding the learning of visual features that are beneficial for adaptation.To solve the problem, we propose semantic entropy to quantify the semantic information contained in visual features, and design SEmantic ENtropy guided Domain-aware Attention (SEEN-DA) to adaptively refine visual features with the semantic information of two domains.Semantic entropy reflects the importance of features based on semantic information, which can serve as attention to select discriminative visual features and suppress semantically irrelevant redundant information.Guided by semantic entropy, we introduce domain-aware attention modules into the visual encoder in SEEN-DA.It utilizes an inter-domain attention branch to extract domain-invariant features and eliminate redundant information, and an intra-domain attention branch to supplement the domain-specific semantic information discriminative on each domain.Comprehensive experiments validate the effectiveness of SEEN-DA, demonstrating significant improvements in cross-domain object detection performance.