Centrifugal compressors used for transporting nature gas are usually equipped with dry gas seals. The working medium of the seal is usually the delivered gas, that is, natural gas. In this paper, the natural gas viscosity-pressure equation is derived from the Pederson mixed gas viscosity model and Lucas viscosity-pressure model, and the real gas property of natural gas is expressed by Redlich-Kwong equation. The gas film pressure governing equations proposed by Muijderman for narrow grooves are modified and solved for the seal faces. The influences of natural gas viscosity-pressure effect on the sealing characteristics, such as leakage rate and opening force, of spiral groove dry gas seal are analyzed. Results show that the viscosity-pressure effect has significant influence on spiral groove dry gas seal. This effect reduces the leakage rate but increases the opening force, compared to the situation without considering the viscosity-pressure effect. With the pressure up to 4MPa, the viscosity-pressure effect of natural gas is weak and negligible. As the pressure increases, the viscosity-pressure effect increases. At 12MPa, the relative deviations of leakage rate and opening force caused by the viscosity-pressure effect are respectively -30.6% and 1.65%. Therefore, the analyses indicate that the viscosity-pressure effect of nature gas needs to be considered when used in high pressure situation.