Log-based anomaly detection is a essential task for ensuring the reliability and performance of software systems. However, the performance of existing anomaly detection methods heavily relies on labeling, while labeling a large volume of logs is highly challenging. To address this issue, many approaches based on transfer learning and active learning have been proposed. Nevertheless, their effectiveness is hindered by issues such as the gap between source and target system data distributions and cold-start problems. In this paper, we propose LogAction, a novel log-based anomaly detection model based on active domain adaptation. LogAction integrates transfer learning and active learning techniques. On one hand, it uses labeled data from a mature system to train a base model, mitigating the cold-start issue in active learning. On the other hand, LogAction utilize free energy-based sampling and uncertainty-based sampling to select logs located at the distribution boundaries for manual labeling, thus addresses the data distribution gap in transfer learning with minimal human labeling efforts. Experimental results on six different combinations of datasets demonstrate that LogAction achieves an average 93.01% F1 score with only 2% of manual labels, outperforming some state-of-the-art methods by 26.28%. Website: https://logaction.github.io/