The geological permeability coefficients are the crucial parameters for accurately analyzing the seepage in hydraulic engineering. To address the issues of low efficiency and accuracy of conventional inversion approaches, this research utilized a combination of the finite element forward model and orthogonal experimental design to construct a sample set for the permeability coefficient inversion. Then, a permeability calculation surrogate model based on the random forest (RF) algorithm was developed. Subsequently, the grey wolf optimization (GWO) algorithm was introduced to develop an intelligent inversion method based on RF-GWO. Taking the Z pumped storage power station as the case study, it is found that the water level prediction outcomes of the RF model are closely aligned with the actual measured values at each borehole, with the performance surpassing CART and BP models. The optimal geological permeability coefficient calculated by GWO performs excellently in the borehole water level inversion, with a maximum relative error of 0.42%, thereby satisfying the required accuracy for engineering applications. The calculated natural seepage field distribution conforms to the general distribution patterns of mountainous seepage fields. Therefore, the proposed inversion model can rapidly and precisely predict the geological permeability coefficient in the project area, demonstrating significant engineering practicality and value.