Domain generalization models aim to learn cross-domain knowledge from source domain data, to improve performance on unknown target domains. Recent research has demonstrated that diverse and rich source domain samples can enhance domain generalization capability. This paper argues that the impact of each sample on the model's generalization ability varies. Despite its small scale, a high-quality dataset can still attain a certain level of generalization ability. Motivated by this, we propose a domain-adversarial active learning (DAAL) algorithm for classification tasks in domain generalization. First, we analyze that the objective of tasks is to maximize the inter-class distance within the same domain and minimize the intra-class distance across different domains. To achieve this objective, we design a domain adversarial selection method that prioritizes challenging samples. Second, we posit that even in a converged model, there are subsets of features that lack discriminatory power within each domain. We attempt to identify these feature subsets and optimize them by a constraint loss. We validate and analyze our DAAL algorithm on multiple domain generalization datasets, comparing it with various domain generalization algorithms and active learning algorithms. Our results demonstrate that the DAAL algorithm can achieve strong generalization ability with fewer data resources, thereby reducing data annotation costs in domain generalization tasks.