In the prosperous development of terahertz (THz) metamaterials, Fano resonances have gained attention due to their potential applications in ultrasensitive systems. The performance of Fano resonance is directly influenced by the geometrical parameters of the element structure. However, the traditional design rules for Fano resonances in metamaterials rely on an empirical trial-and-error strategy, necessitating significant effort to achieve optimal results. To address this issue, we propose a design method in this study that utilizes the finite integration technique in time domain (FITD) along with a multi-objective optimization genetic algorithm for the intelligent design of metamaterial structures exhibiting the Fano resonance phenomenon. The FITD method is primarily used to calculate the Fano resonance with different metamaterial geometric structure parameters, while the genetic algorithm efficiently selects the optimal solution. Our method, characterized by high efficiency and complete independence from prior knowledge, could offer a new design technique for metamaterials with specific functions, thereby contributing to the development of THz applications.