The latest proposed Broad Learning System (BLS) demonstrates an efficient and effective learning capability in many machine learning problems. In this paper, we apply the BLS to address transductive transfer learning problems, where the training (source) and test (target) data are drawn from the different but related distributions, which is a.k.a domain adaptation. We aim at learning from source data a well performing classifier on a different (but related) target data. A unified domain adaptation framework based on the BLS is developed for improving its transfer learning capability without loss of the computational efficiency. Two algorithms including BLS based source domain adaptation (BLS-SDA) and BLS based target domain adaptation (BLS-TDA) are proposed under this framework. Experiments on benchmark datasets show that our approach outperforms several existing domain adaptation methods while maintains high efficiency.