The establishment of flying ad hoc networks (FANETs) can effectively meet the networking communication requirements of UAV cluster operation, but compared with the traditional mobile ad hoc network, flying ad hoc network has the characteristics of faster node movement and dynamic network topology. To solve the problem of network performance degradation caused by frequent link disconnection, this paper proposes a high stability routing protocol based on load sensing and pseudo gossip mechanism. Network congestion and node mobility are two main factors affecting path stability. In order to solve the problem of network congestion, a pseudo rumor limited flooding mechanism based on node load prediction is proposed. In the process of initiating routing requests, the node forwarding probability is dynamically adjusted to balance the network load and reduce the control overhead. Aiming at the high mobility characteristics of UAV nodes, a joint measurement index of link stability is proposed based on the received packet signal power strength. Simulation results show that, compared with AODV protocol and other improved protocols, this protocol can effectively reduce the network control overhead, improve the packet delivery rate, reduce the average end-to-end delay, significantly improve the network performance, and enhance the real-time and reliability of data transmission.