The viscosity coefficient of methanol vapor was measured at low densities by means of an all-quartz oscillating-disk viscometer of high precision. The relative measurements were performed along 10 isochores at densities from (0.004 to 0.050) mol center dot dm(-3) in the temperature range between (298 and 603) K. The uncertainty is estimated to be +/- 0.2 % at room temperature, increasing up to +/- 0.3 % at higher temperatures. Isothermal values recalculated from the original experimental data were evaluated with a first-order expansion for the viscosity in terms of density. A reasonable agreement with experimental values from the literature was found for those of Golubev and Likhachev (up to 1 % higher) measured with a capillary viscometer in an extended temperature range up to high pressures. The new results, some older ones obtained in our laboratory, and those of Golubev and Likhachev are used to model the viscosity of methanol vapor at moderately low densities. Whereas an individual correlation according to the extended theorem of corresponding states was necessary to represent the zero-density viscosity coefficient within its uncertainty, the Rainwater-Friend theory proved to be suitable for the description of the second viscosity virial coefficient. In addition, viscosity values of the saturated vapor were determined at low temperatures (299 to 339 K). They are in reasonable good consistency with values of Golubev determined at higher temperatures (373 to 513 K).