Existing methods for learning Bayesian network structures run into the computational and statistical problems because of the following two reasons: a large number of variables and a small sample size for enormous variables. Adopting the divide and conquer strategies, we propose a novel algorithm, called block learning algorithm, to learn Bayesian network structures. The method partitions the variables into several blocks that are overlapped with each other. The blocks are learned individually with some constraints obtained from the learned overlap structures. After that, the whole network is recovered by combining the learned blocks. Comparing with some typical learning algorithms on golden Bayesian networks, our proposed methods are efficient and effective. It shows a large potential capability to be scaled up.