Existing algorithms for learning Bayesian network (BN) require a lot of computation on high dimensional itemsets, which affects accuracy especially on limited datasets and takes up a large amount of time. To alleviate the above problem, we propose a novel BN learning algorithm OMRMRG, Ordering-based Max Relevance and Min Redundancy Greedy algorithm. OMRMRG presents an ordering-based greedy search method with a greedy pruning procedure, applies Max-Relevance and Min-Redundancy feature selection method, and proposes Local Bayesian Increment function according to Bayesian Information Criterion (BIC) formula and the likelihood property of overfitting. Experimental results show that OMRMRG algorithm has much better efficiency and accuracy than most of existing BN learning algorithms on limited datasets.