A vibrating-wire viscometer has been formed from cold-drawn centerless-ground tungsten wire of a nominal radius of 0.15 mm. The working equations for the vibrating-wire viscometer require values of the wire radius and internal damping. The radius of the wire was determined by contact micrometry combined with laser interferometry while the internal damping was obtained from measurements in vacuum. With these values, the vibrating-wire instrument provides an absolute measure of the viscosity of liquids. The apparatus has been used to measure the viscosity of water at a temperature of 293.15 K and a pressure of 101.325 kPa. The result obtained differs by less than 0.03% from the International Organization for Standardization (ISO) recommendation (ISO/TR 3666, 1998) for the viscosity of water. The relative expanded (k = 2) uncertainty of the viscosity obtained from the vibrating-wire viscometer is +/- 0.9%, that is, 3.6 times greater than the relative uncertainty of the ISO recommendation. This work illustrates, for the first time, that a vibrating wire can be operated as an absolute viscometer for liquids.