Active Domain Adaptation (ADA) selects a restricted quantity of target samples to label to effectively adapt a model trained on a source domain to a target domain. In this process, uncertainty and representativeness are two crucial principles. Strategies focused on uncertainty seek to choose samples where the model’s predictions are less certain, whereas those centered on representativeness aim to pick samples that better reflect the overall data distribution. Existing ADA methods incorporate the concept of targetness to measure the representativeness of characteristics in the target domain, yet their predictive uncertainty often relies on the predictions of deterministic models, which can be prone to miscalibration when dealing with data exhibiting distribution shifts. To this end, a Dirichlet-Based Local Inconsistency (DBLI) method is proposed, which introduces a Dirichlet prior distribution into model prediction and combines the local inconsistency criterion of query data. A two-stage selection strategy is devised to combine the prediction uncertainty of samples with the local inconsistency of Dirichlet quantization in each round of selection. In addition, an invertible neural network based homeomorphism is constructed to bring the source and target data into alignment in separate spaces, facilitating domain adaptation. Extensive experiments are performed on the two commonly used benchmark datasets: Office-31 and Office-Home, resulting in a 4.3% improvement in accuracy and 3%, correspondingly, validating the superiority of DBLI.