<p>Many oversampling algorithms for imbalanced data learning take new samples from a range enclosed by several original minority-class samples regardless of the distribution of the majority-class samples, and thus the oversampling results could misguide the downstream classifier. To overcome this limitation, this paper introduces the Bézier curves guided by minimum spanning trees (MSTs) to form a new oversampling algorithm, called MST-Bézier, for imbalanced data learning. MSTs capture the intrinsic structural characteristics of the minority-class samples. Bézier curves provide the oversampling ranges that potentially lead to a reasonable classification margin. The end points of an MST edge and the majority-class samples lying in their nearest neighbours serve as the controlling points of each Bézier curve. Taking advantage of these characteristics, the oversampling results provided by MST-Bézier are close to the potential classification margin without falling in the interior of majority-class samples. The numerical experiments support the effectiveness of the proposed MST-Bézier, and show that the downstream classifiers associated with MST-Bézier outperform the ones associated with baseline oversampling algorithms.</p>