Ordinal multi-instance learning (OMIL) deals with the weak supervision scenario wherein instances in each training bag are not only multi-class but also have rank order relationships between classes, such as breast cancer, which has become one of the most frequent diseases in women. Most of the existing work has generally been to classify the region of interest (mass or microcalcification) on the mammogram as either benign or malignant, while ignoring the normal mammogram classification. Early screening for breast disease is particularly important for further diagnosis. Since early benign lesion areas on a mammogram are very similar to normal tissue, three classifications of mammograms for the improved screening of early benign lesions are necessary. In OMIL, an expert will only label the set of instances (bag), instead of labeling every instance. When labeling efforts are focused on the class of bags, ordinal classes of the instance inside the bag are not labeled. However, recent work on ordinal multi-instance has used the traditional support vector machine to solve the multi-classification problem without utilizing the ordinal information regarding the instances in the bag. In this paper, we propose a method that explicitly models the ordinal class information for bags and instances in bags. Specifically, we specify a key instance from the bag as a positive instance of bags, and design ordinal minimum uncertainty loss to iteratively optimize the selected key instances from the bags. The extensive experimental results clearly prove the effectiveness of the proposed ordinal instance-learning approach, which achieves 52.021% accuracy, 61.471% sensitivity, 47.206% specificity, 57.895% precision, and an 59.629% F1 score on a DDSM dataset.