In dynamic outdoor environments characterized by turbulent airflow and intermittent odor plumes, robotic odor plume tracking remains challenging, because existing algorithms heavily rely on manually tuning or learning from expert experience, which are hard to implement in an unknown environment. In this paper, a multi-continuous-output Takagi–Sugeno–Kang fuzzy system was designed and tuned with reinforcement learning to solve the robotic odor source localization problem in dynamic odor plumes. Based on the Lévy Taxis plume tracking controller, the proposed fuzzy system determined the parameters of the controller based on the robot’s observation and guided the robot to turn and move towards the odor source at each searching step. The trained fuzzy system was tested in simulated filament-based odor plumes dispersed by a changing wind field. The results showed that the performance of the proposed fuzzy system-based controller trained with reinforcement learning can achieve a similar success rate and higher efficiency compared with a manually tuned and well-designed fuzzy system-based controller. The fuzzy system-based plume tracking controller was also validated through real robotic experiments.