As an effective and efficient discriminative learning method, the broad learning system (BLS) has received increasing attention due to its outstanding performance without large computational resources. The standard BLS is derived under the minimum mean square error (MMSE) criterion, while MMSE is with poor performance when dealing with imbalanced data. However, imbalanced data are widely encountered in real-world applications. To address this issue, a novel cost-sensitive BLS algorithm (CS-BLS) is proposed. In the CS-BLS, many variations can be adopted, and CS-BLS with weighted cross-entropy is analyzed in this paper. Weighted penalty factors are used in CS-BLS to constrain the contribution of each sample in different classes. The samples in minor classes are allocated higher weights to increase their contributions. Four different weight calculation methods are adopted to the CS-BLS, and thus, four CS-BLS methods are proposed: Log-CS-BLS, Lin-CS-BLS, Sqr-CS-BLS, and EN-CS-BLS. Experiments based on artificially imbalanced datasets of MNIST and small NORB are firstly conducted and compared with the standard BLS. The results show that the proposed CS-BLS methods have better generalization and robustness than the standard BLS. Then, experiments on a real ultrasound breast image dataset are conducted, and the results demonstrate that the proposed CS-BLS methods are effective in actual medical diagnosis.