In this paper, we propose a novel end-to-end unsupervised deep domain adaptation model for adaptive object detection by exploiting multi-label object recognition as a dual auxiliary task. The model exploits multi-label prediction to reveal the object category information in each image and then uses the prediction results to perform conditional adversarial global feature alignment, such that the multi-modal structure of image features can be tackled to bridge the domain divergence at the global feature level while preserving the discriminability of the features. Moreover, we introduce a prediction consistency regularization mechanism to assist object detection, which uses the multi-label prediction results as an auxiliary regularization information to ensure consistent object category discoveries between the object recognition task and the object detection task. Experiments are conducted on a few benchmark datasets and the results show the proposed model outperforms the state-of-the-art comparison methods.