In response to the issue of load imbalance caused by the multi-controller architecture in complex Software Defined Network (SDN) structures within large data centers, a switch migration strategy based on reinforcement learning is proposed. First, the switch migration problem is modeled as a combinatorial optimization problem, taking into account both load balancing and the distribution of controller loads. Next, we optimize the Soft Actor-Critic (SAC) algorithm by incorporating a priority migration mechanism based on a SumTree, aiming to maximize improvements in load balancing while employing a strategy that incurs minimal migration overhead. A global control plane connection is established through a server to facilitate switch migration based on load conditions, ultimately achieving load balancing among controllers. Simulation results indicate that this strategy effectively realizes load balance according to load states. In a simple load environment, load balancing improved by 17.34%; in a complex load environment, the performance enhancement was even more significant, reaching 74.45%, while also demonstrating certain advantages in terms of migration overhead.