Dry gas face seal (DGS) is one of non-contacting mechanical face seals that can be applied to most of the gas transportation machines. It is very important for designing the seal correctly to understand the seal behavior, especially gas film stiffness and leakage rate. The finite element method was used to solve the two-dimensional Reynolds equation for getting the gas film pressure distribution between the two faces of a spiral-groove face seal (S-DGS). The static sealing performances, such as gas film stiffness and leakage rate were determined. Subsequently the effects of seal geometrical parameters pairwise changed on the behavior of a S-DGS were analyzed, which mainly refer to the ratio of groove depth to gas film thickness, the length ratio of the spiral-groove to the seal dam, and the spiral-groove angle. The recommended geometrical parameters were presented, which can assume large film stiffness while the leakage rate is very small.