Low Earth orbit (LEO) satellites that can be used as computing nodes are an important part of future communication networks. However, growing user demands, scarce channel resources and unstable satellite–ground links result in the challenge to design an efficient channel allocation algorithm for the LEO satellite network. Edge computing (EC) provides sufficient computing power for LEO satellite networks and makes the application of reinforcement learning possible. In this paper, an adaptive dynamic channel allocation algorithm based on a temporal–spatial correlation analysis for LEO satellite networks is proposed. First, according to the user mobility model, the temporal–spatial correlation of handoff calls is analyzed. Second, the dynamic channel allocation process in the LEO satellite network is formally described as a Markov decision process. Third, according to the temporal–spatial correlation, a policy for different call events is designed and online reinforcement learning is used to solve the channel allocation problem. Finally, the simulation results under different traffic distributions and different traffic intensities show that the proposed algorithm can greatly reduce the rejection probability of the handoff call and then improve the total performance of the LEO satellite network.