UAl 3 is a typical heavy-electron compound which belongs to the valence-fluctuation regime. The major experimental frequency branches of the de Haas-van Alphen effect is explained reasonably well by the large hole sheets of the Fermi surface which were derived on the basis of an itinerant 5 f -electron model. In particular, it is shown by visualizing the extremal electron orbits that one of the major experimental frequency branches, i.e., the branch , can be explained by those orbits which run through the multiplyconnected large hole sheet.