Domain Adaptation aiming to learn a transferable feature between different but related domains has been well investigated and has shown excellent empirical performances. Previous works mainly focused on matching the marginal feature distributions using the adversarial training methods while assuming the conditional relations between the source and target domain remained unchanged, $i.e.$, ignoring the conditional shift problem. However, recent works have shown that such a conditional shift problem exists and can hinder the adaptation process. To address this issue, we have to leverage labelled data from the target domain, but collecting labelled data can be quite expensive and time-consuming. To this end, we introduce a discriminative active learning approach for domain adaptation to reduce the efforts of data annotation. Specifically, we propose three-stage active adversarial training of neural networks: invariant feature space learning (first stage), uncertainty and diversity criteria and their trade-off for query strategy (second stage) and re-training with queried target labels (third stage). Empirical comparisons with existing domain adaptation methods using four benchmark datasets demonstrate the effectiveness of the proposed approach.