We present a measurement of the cross section for Z production times the branching fraction to tau leptons, sigma·Br(Z-->tau+tau-), in p[overline p] collisions at sqrt(s)=1.96 TeV in the channel in which one tau decays into µnuµnutau, and the other into hadrons+nutau or enuenutau. The data sample corresponds to an integrated luminosity of 226 pb-1 collected with the D0 detector at the Fermilab Tevatron collider. The final sample contains 2008 candidate events with an estimated background of 55%. From this we obtain sigma·Br(Z-->tau+tau-)=237±15(stat)±18(sys)±15(lum)pb, in agreement with the standard model prediction.