Key distribution is a challenging issue for Wireless Sensor Networks (WSNs) because sensor nodes are built from resource-constrained devices that carry limited-power batteries. Thus, a key distribution scheme for WSNs must be efficient — at least in terms of energy consumption and storage. However, most proposed key distribution schemes in the literature ignore energy consumption and do not consider efficiency. Therefore, we propose an efficient key distribution protocol that is designed to suit resource-constrained devices such as WSNs. In this research, we utilized OPNET Modeler to create and to model a wireless sensor node and then developed a wireless sensor network. Our sensor model not only calculate the energy consumption of a node transceiver but also it computes the energy consumption that is caused by wireless channel effects. Furthermore, we utilized an automatic cryptographic protocol verifier, ProVerif, to verify the security properties of the proposed protocol. The findings show that the proposed protocol is secure and more efficient compared to key distribution schemes in the literature.