A vibrating-wire viscometer of very high precision was used to measure the viscosity coefficient of gaseous sulfur hexafluoride. The experimental data were taken at subcritical temperatures of (300 and 316) K up to 90% of the saturated vapor pressure and at supercritical temperatures of (321, 333.15, 350, 375, 400, and 425) K at pressures up to 20 MPa. The measuring values were evaluated using an equation of state by Wagner and Kurzeja. The reproducibility is ±(0.05 to 0.1)%, whereas the total uncertainty is estimated to be ±(0.25 to 0.4)% with a distinct increase approaching the critical region. The viscosity values of the isotherms were evaluated using a power series expansion in terms of density without and with logarithmic term. The existence of a quadratic term that is logarithmic in density could not be proven. A comparison with data from the literature shows that the new values agree in the low-density range within ± 0.2% and at higher densities apart from the near-critical region within ± 0.3% with the most reliable data.