In practice, some bugs have more impact than others and thus deserve more immediate attention. Due to tight schedule and limited human resources, developers may not have enough time to inspect all bugs. Thus, they often concentrate on bugs that are highly impactful. In the literature, high-impact bugs are used to refer to the bugs which appear at unexpected time or locations and bring more unexpected effects (i.e., surprise bugs), or break pre-existing functionalities and destroy the user experience (i.e., breakage bugs). Unfortunately, identifying high-impact bugs from thousands of bug reports in a bug tracking system is not an easy feat. Thus, an automated technique that can identify high-impact bug reports can help developers to be aware of them early, rectify them quickly, and minimize the damages they cause. Considering that only a small proportion of bugs are high-impact bugs, the identification of high-impact bug reports is a difficult task. In this paper, we propose an approach to identify high-impact bug reports by leveraging imbalanced learning strategies. We investigate the effectiveness of various variants, each of which combines one particular imbalanced learning strategy and one particular classification algorithm. In particular, we choose four widely used strategies for dealing with imbalanced data and four state-of-the-art text classification algorithms to conduct experiments on four datasets from four different open source projects. We mainly perform an analytical study on two types of high-impact bugs, i.e., surprise bugs and breakage bugs. The results show that different variants have different performances, and the best performing variants SMOTE (synthetic minority over-sampling technique) + KNN (K-nearest neighbours) for surprise bug identification and RUS (random under-sampling) + NB (naive Bayes) for breakage bug identification outperform the F1-scores of the two state-of-the-art approaches by Thung et al. and Garcia and Shihab.