Distributed multi-controller deployment is a reliable method of achieving the scalability in Software-Defined Networking (SDN). With the explosive growth of network traffic, distributed SDN network is facing the problem of load imbalance among multiple controllers due to the dynamic change of network traffic. However, this problem is solved by switch migration considering con-troller load and delay, which will lead to high migration cost and low migration efficiency. Therefore, in this paper, a Fuzzy Satisfaction-based Switch Migration (FSSM) strategy is proposed to load balancing of distributed controllers. First, to monitor the controller load, the balancing judgment matrix and switch selection degree is introduced to select emigration domain and migrating switches. Second, migration cost and load balancing rate are considered as the main factors of load balancing. They are transformed into a migration competition model, which is used to compete for optimization rights. Third, the model is quickly solved by using the improved ant colony algorithm to select immigration domain. Finally, simulation results show that compared with existing migration strategies, FSSM strategy not only ensures the load balancing rate, but also reduces the migration cost by about 26.8% and the average response time of controllers by about 0.33 s when the network changes dynamically.