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Cross domain object detection is a realistic and challenging task in the wild. It suffers from performance degradation due to large shift of data distributions and lack of instance-level annotations in the target domain. Existing approaches mainly focus on either of these two difficulties, even though they are closely coupled in cross domain object detection. To solve this problem, we propose a novel Target-perceived Dual-branch Distillation (TDD) framework. By integrating detection branches of both source and target domains in a unified teacher-student learning scheme, it can reduce domain shift and generate reliable supervision effectively. In particular, we first introduce a distinct Target Proposal Perceiver between two domains. It can adaptively enhance source detector to perceive objects in a target image, by leveraging target proposal contexts from iterative cross-attention. Afterwards, we design a concise Dual Branch Self Distillation strategy for model training, which can progressively integrate complementary object knowledge from different domains via self-distillation in two branches. Finally, we conduct extensive experiments on a number of widely-used scenarios in cross domain object detection. The results show that our TDD significantly outperforms the state-of-the-art methods on all the benchmarks. Our code and model will be available at https://github.com/Feobi1999/TDD.