Cross-domain object detection is more challenging than object classification since multiple objects exist in an image and the location of each object is unknown in the unlabeled target domain. As a result, when we adapt features of different objects to enhance the transferability of the detector, the features of the foreground and the background are easy to be confused, which may hurt the discriminability of the detector. Besides, previous methods focused on category adaptation but ignored another important part for object detection, i.e., the adaptation on bounding box regression. To this end, we propose D-adapt, namely Decoupled Adaptation, to decouple the adversarial adaptation and the training of the detector. Besides, we fill the blank of regression domain adaptation in object detection by introducing a bounding box adaptor. Experiments show that \textit{D-adapt} achieves state-of-the-art results on four cross-domain object detection tasks and yields 17\% and 21\% relative improvement on benchmark datasets Clipart1k and Comic2k in particular.