Bayesian network is a popular machine learning tool for modeling uncertain dependence relationships among the random factors of a domain. It represents the relations qualitatively by using a directed acyclic graph (DAG) and quantitatively by using a set of conditional probability distributions. Several exact algorithms for learning optimal Bayesian networks from data have been developed recently. However, these algorithms are still inefficient to some extent. This is not surprising because learning Bayesian network has been proven to be an NP-Hard problem. Based on a critique of these algorithms, this thesis introduces a new algorithm based on heuristic search for learning optimal Bayesian.