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Wireless ad hoc network is a wireless communication network that does not require preset infrastructure. It consists of a group of mobile terminals equipped with wireless transceiver devices, forming a decentralized, multi-hop, and self-organizing network. The neighbor discovery issue in the Medium Access Control (MAC) protocol of ad hoc networks is crucial to network performance. Aiming at the needs of narrow-beam and high-dynamic scenarios in airborne wireless ad hoc networks, a novel network-synchronized MAC layer protocol algorithm (FDBC-ND) is proposed. This algorithm ensures the alignment speed of antennas and the synchronization accuracy of time based on the characteristics of narrow-beam and high-dynamic millimeter-wave communication while satisfying the communication requirements of airborne networking. The neighbor discovery algorithm is verified through simulation experiments. Simulation results show that when the beam width of the antenna is 12° and the number of network nodes is 20, the average neighbor discovery time of the FDBC-ND algorithm is approximately 11.85s. It can be well applied to the scenario of airborne directional narrow-beam and high dynamics.