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Low-earth orbit (LEO) satellite networks are an important part of the sixth-generation mobile communication system (6G) network, which overcomes the blind spots in ground-based station coverage. However, the limited onboard computing capability and battery capacity cause the problems of extended mission duration and high-energy consumption; therefore, edge computing is introduced in LEO satellite networks, and its key technology is computational offloading. To address the problems of dynamic changes in the intersatellite environment and high-dimensional action space during computational offloading, we propose a genetic algorithm (GA) and deep deterministic policy gradient (DDPG)-based offloading algorithm for edge computing in space-based LEO satellite networks—the GA-DDPG algorithm. The constant change in a satellite edge computing environment will result in sparse rewards (system overhead) and a lack of DDPG exploration. In this study, a GA is introduced into the DDPG algorithm. First, the selection operator of the GA is used to enable the DDPG algorithm to adapt to a changing satellite environment. Second, to address the problem of unstable convergence of the DDPG algorithm owing to the increasing dimension of the action space, the diversity exploration and redundancy of the GA population are used to improve the stability of the convergence of the DDPG algorithm. In this study, a system model, including a space-based LEO satellite constellation structure, mission model, computational model, and load model, is constructed; in addition, a system overhead, weighted by the residual rate of battery energy of edge satellites, is designed to model the problems of minimization of mission delay, minimization of mission energy consumption, and optimization of computational resource allocation as a Markov process. First, the offloading algorithm obtains edge satellites that are visible to the local satellites by analyzing the constraints for establishing links between the satellites. Second, the channel is modeled, and the intersatellite path loss and Doppler shift are modeled, following which the intersatellite transmission rate is obtained. Subsequently, information on the computational capacity and battery energy remaining of each satellite is obtained through the intersatellite link, and a monitoring cycle is set to timely correct the satellite network topology structure. Third, the intersatellite link parameters and mission information are transmitted to the GA-DDPG computational offloading algorithm; various strategies are generated using the GA; elite strategies are input into the replay buffer of the DDPG algorithm; the less adapted strategies are input into the actor network of the DDPG algorithm; the strategies in the replay buffer are used to train their strategies, and the strategies with improved adaptation after training are inserted into the GA population, following which the optimal strategy is determined from the strategy population, and the strategy is updated using the GA to generate the next generation strategy population. The simulation results demonstrate that the GA-DDPG unloading algorithm reduces the computational load of space-based low-orbit satellite networks, and the algorithm confirms its stability (low volatility) through the variance of the computational load. The delay and energy consumption are lower than those of the DDPG and GA unloading algorithms, respectively, increasing the convergence speed and stability of the algorithm compared with the DDPG unloading algorithm.