Recently machine learning is used in various applications and has shown success. Machine learning is good at learning the overall characteristics of massive training data. However, for real-world applications, training data often include multiple domains, and some domains have higher importance or risks. In this paper, we first propose a new problem setting: machine learning with blind imbalanced domains. In the proposed problem, the domain assignment of samples is unknown and imbalanced in the training data, and the performance is evaluated for each domain in the test data. Second, we propose an approach for that problem in classification tasks. The proposed approach combines center loss and weighted mini-batch sampling based on distances between samples and centroids in the deep feature space. Experiments on one minor domain and two minor domain settings using three handwritten digit databases (MNIST, EMNIST, and USPS) show that our proposed approach outperforms possible solutions using related methods. Remarkably our approach improves the accuracy in the minor domain by more than 1% on average. Furthermore, it can be inductively estimated that our proposed approach works on multiple domains given the successful results on one and two minor domains.