A two-dimensional Reynolds equation was established for isothermal compressible gas between the two faces of a dry gas face seal with both spiral grooves and an inner annular groove onto the hard face. The opening force, the leakage rate, the axial film stiffness and the film stiffness to leakage ratio were calculated by finite element method. The comparisons with the sealing performances of a typical gas face seal only with spiral grooves onto its hard face were made. The effects of the face geometric parameters on the static behavior of such a seal were analyzed. The optimization principle for geometric parameters of a dry gas face seals with spiral grooves and an inner annular groove was presented. The recommended geometric parameters of spiral grooves and circular groove presented by optimization can ensure larger axial stiffness while lower leakage rates.