To improve the sealing performance of the micro-textured floating ring seal with gas as the lubricating medium, the effect of elliptical micro-textured holes on the hydrodynamic lubrication of the floating ring gas film seal was studied under different working parameters to provide the theory for the optimal design of the floating ring gas film seal. Based on the gas lubrication theory, the physical equations were built to express the gas flow state in the gap of the textured sealing rings. The established governing equations were solved numerically by the finite difference method. A numerical simulation of the hydrodynamic pressure distribution was modeled in the sealing gap of the floating ring seal. The maximum gas opening force and minimum leakage rate were selected as the optimal criteria for the structural parameters. The effect of the structural parameters of the elliptical micro-textured holes on the sealing performance under specific working conditions was analyzed, and then the optimal range of structural parameters for better sealing performance was obtained. The numerical solution of the established theoretical model of the lubricating gas flow in the sealing gap of micro-textured floating ring gas film had a little error with the comparison model, which could effectively analyze the hydrodynamic lubrication performance of the lubricating gas flow state. The hydrodynamic effect and the gas opening force could be strengthened with the increasing rotational speed and the inlet pressure of the medium gas. The leakage rate of the medium gas increased significantly with the increase of the inlet pressure, the leakage rate decreased with the improvement of the rotational speed, but the decrease was relatively small. The main affecting factors of the geometrical parameters of elliptical micro-textured holes on the gas film opening force of the floating ring gas film seal were sorted in order:area ratio > shape ratio > texture depth > rotational inclination angle. The primary affecting factors on the medium gas leakage rate of the sealing device were ranked in order:texture depth > shape ratio > area ratio > rotational inclination angle. Within the analysis range of rotational speed and inlet gas pressure, the lubricating effect and sealing performance of the floating ring gas film seal were affected by the geometrical parameters of the micro-textured holes on the surface of the shaft sleeve. The specific structural parameters of the elliptical micro-textured holes recommended to be preferentially would be used as follows:shape ratio γ=3∶1, area ratio Sp=11%, rotational inclination angle β=0°, and micro-textured hole depth ht=1 μm, to obtain excellent sealing performance. The existence of the elliptical micro- textured holes on the surface of the shaft sleeve can improve the sealing performance of the floating ring gas film seal. Selecting appropriate surface texture parameters can achieve the effect of reducing friction and improving the lubrication. The gas opening force of the eccentric floating ring gas film seal is enhanced when the leakage rate of the sealing device decreases. The results of this study can provide a theoretical reference for the processing and manufacturing of the floating ring gas film seal.