Training a spoofing countermeasure (CM) that generalizes to various unseen data is desired but challenging. While methods such as data augmentation and self-supervised learning are applicable, the imperfect CM performance on diverse test sets still calls for additional strategies. This study took the initiative and investigated CM training using active learning (AL), a framework that iteratively selects useful data from a large pool set and fine-tunes the CM. This study compared a few methods to measure the data usefulness and the impact of using different pool sets collected from various sources. The results showed that the AL-based CMs achieved better generalization than our strong baseline on multiple test tests. Furthermore, compared with a top-line CM that simply used the whole data pool set for training, the AL-based CMs achieved similar performance using less training data. Although no single best configuration was found for AL, the rule of thumb is to include diverse spoof and bona fide data in the pool set and to avoid any AL data selection method that selects the data that the CM feels confident in.