This paper proposes a novel federated edge learning (FEEL) algorithm, FEDMEGA, tailored for low-earth-orbit (LEO) mega-constellation networks. The main challenges in applying FEEL to LEO networks include the high mobility of satellites, short ground-to-satellite link (GSL) durations, and the need for frequent model transmission between satellites and the ground. FEDMEGA addresses these challenges by leveraging inter-satellite links (ISLs) for intra-orbit model aggregation, reducing reliance on GSLs and improving transmission efficiency. The algorithm employs a ring all-reduce mechanism for intra-orbit aggregation and a network flow-based transmission scheme for global model aggregation. Theoretical convergence analysis is provided, showing that FEDMEGA achieves a 30% improvement in convergence rate compared to existing satellite FEEL algorithms. Simulation results demonstrate that FEDMEGA outperforms existing methods in terms of convergence speed and prediction accuracy. The proposed framework includes on-board local training, intra-orbit aggregation, and global aggregation and broadcasting, with a focus on minimizing GSL utilization and reducing transmission latency. The algorithm is designed to handle non-convex loss functions and non-IID data distributions, ensuring efficient and effective model training in LEO networks.This paper proposes a novel federated edge learning (FEEL) algorithm, FEDMEGA, tailored for low-earth-orbit (LEO) mega-constellation networks. The main challenges in applying FEEL to LEO networks include the high mobility of satellites, short ground-to-satellite link (GSL) durations, and the need for frequent model transmission between satellites and the ground. FEDMEGA addresses these challenges by leveraging inter-satellite links (ISLs) for intra-orbit model aggregation, reducing reliance on GSLs and improving transmission efficiency. The algorithm employs a ring all-reduce mechanism for intra-orbit aggregation and a network flow-based transmission scheme for global model aggregation. Theoretical convergence analysis is provided, showing that FEDMEGA achieves a 30% improvement in convergence rate compared to existing satellite FEEL algorithms. Simulation results demonstrate that FEDMEGA outperforms existing methods in terms of convergence speed and prediction accuracy. The proposed framework includes on-board local training, intra-orbit aggregation, and global aggregation and broadcasting, with a focus on minimizing GSL utilization and reducing transmission latency. The algorithm is designed to handle non-convex loss functions and non-IID data distributions, ensuring efficient and effective model training in LEO networks.