Recently, active learning has been applied to recommendation to deal with data sparsity on a single domain. In this paper, we propose an active learning strategy for recommendation to alleviate the data sparsity in a multi-domain scenario. Specifically, our proposed active learning strategy simultaneously consider both specific and independent knowledge over all domains. We use the expected entropy to measure the generalization error of the domain-specific knowledge and propose a variance-based strategy to measure the generalization error of the domain-independent knowledge. The proposed active learning strategy use a unified function to effectively combine these two measurements. We compare our strategy with five state-of-the-art baselines on five different multi-domain recommendation tasks, which are constituted by three real-world data sets. The experimental results show that our strategy performs significantly better than all the baselines and reduces human labeling efforts by at least 5.6%, 8.3%, 11.8%, 12.5% and 15.4% on the five tasks, respectively.