Securing a sufficient amount of paired data is important to train an image-text retrieval (ITR) model, but collecting paired data is very expensive. To address this issue, in this paper, we propose an active learning algorithm for ITR that can collect paired data cost-efficiently. Previous studies assume that image-text pairs are given and their category labels are asked to the annotator. However, in the recent ITR studies, the importance of category label is decreased since a retrieval model can be trained with only image-text pairs. For this reason, we set up an active learning scenario where unpaired images (or texts) are given and the annotator provides corresponding texts (or images) to make paired data. The key idea of the proposed AL algorithm is to select unpaired images (or texts) that can be hard negative samples for existing texts (or images). To this end, we introduce a novel scoring function to choose hard negative samples. We validate the effectiveness of the proposed method on Flickr30K and MS-COCO datasets.