Anomalously U-rich granites of the so-called Revsund type, associated with W- and Sn-enrichments, occur in the Gunnarn area close to Storuman in northern Sweden. At Rostberget, a swarm of thin undeformed wolframite-bearing greisen veins are situated in the interior of the Joran granite intrusion. We have dated zircons from a sample of the greisen veins with the U-Pb method. The veins are less than 1 cm wide and it is likely that the sample also contains zircons from the immediately surrounding altered granite. The mineralizing event and connected metasomatic processes probably released Zr from the granite which became available for zircon growth processes in the greisen veins. One notable feature, probably due to the greisen-forming processes, is the very high common Pb concentrations characterizing the zircons. By varying the assumed common Pb composition in the calculations, the effect on resulting intercept ages has been evaluated. The obtained age interval (1775-1782 Ma) is typical of formation ages for Revsund granites, which indicates that the mineralization event at Rostberget followed closely upon the granite emplacement. We conclude that the Revsund-type granites, which cover large areas, were generated in a narrow time interval 1790-1775 Ma ago.