A new structure learning approach for Bayesian networks (BNs) based on dual genetic algorithm (DGA) is proposed in this paper. An individual of the population is represented as a dual chromosome composed of two chromosomes. The first chromosome represents the ordering among the BN nodes and the second represents the conditional dependencies among the ordered BN nodes. It is rigorously shown that there is no BN structure that cannot be encoded by the proposed dual genetic encoding and the proposed encoding explores the entire solution space of the BN structures. In contrast with existing GA-based structure learning methods, the proposed method learns not only the topology of the BN nodes, but also the ordering among the BN nodes, thereby, exploring the wider solution space of a given problem than the existing method. The dual genetic operators are closed in the set of the admissible individuals. The proposed method is applied to real-world and benchmark applications, while its effectiveness is demonstrated through computer simulation.