Fuzzy logic controllers (FLCs) are widely used to control complex systems with model uncertainty, such as alternating current motors. The design process of the FLC is generally based on the designer's adjustments on the controller until the desired performance is achieved. However, doing the controller design in this way makes the design process quite difficult and time-consuming, so it is often impossible to make a suitable and successful design. In this study, the output membership functions of the FLC are optimized with heuristic algorithms to reach the best speed control performance of the permanent magnet synchronous motor (PMSM). This paper proposes a new hybrid algorithm called H-GA-GSA, created by combining the advantages of the Genetic Algorithm (GA) and Gravitational Search Algorithm (GSA) to optimize FLC. The paper presents a convenient adjustment and design method for optimizing FLC with heuristic algorithms considered. To evaluate the effectiveness of H-GA-GSA, the proposed hybrid algorithm has been compared with GA and GSA in terms of convergence rate, PMSM speed control performance and electromagnetic torque variations. Optimization performance and results obtained from simulation studies verify that the proposed hybrid H-GA-GSA outperforms GA and GSA.