To ensure that the six-hardpoint positioning system of a 4m silicon carbide （SiC） primary mirror has a sufficiently high natural frequency， the configuration parameters of a six-hardpoint positioning mechanism are optimized. First， dynamic and natural frequency equations of the six-hardpoint positioning system of the primary mirror are derived， and the functional relationship between the configuration parameters of the mechanism， axial stiffness of the hardpoint， mass and inertia of the primary mirror， and natural frequency of the system are established. Next， finite element analysis is used to determine the axial stiffness of the hardpoint used in positioning the mirror. Based on the natural frequency equation and with the goal of maximizing the first-order natural frequency of the mirror system， the configuration parameters of the six-hardpoint positioning mechanism are optimized using a genetic algorithm. Finally， a modal analysis of the mirror system under the optimal configuration is conducted. The axial stiffness of the hardpoint was 33.044 N/μm. Under the optimized configuration parameters， the first-order natural frequency of the 4m SiC primary mirror system reached 30.83 Hz， which is a significant improvement over the initial value. The optimization method can effectively improve the first-order natural frequency of the six-hardpoint positioning system of a primary mirror.