We present a search for lepton-flavor-violating tau decays into three leptons (electrons or muons) using 782 fb(-1) of data collected with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. No evidence for these decays is observed and we set 90% confidence level upper limits on the branching fractions between 1.5 x 10(-8) and 2.7 x 10(-8)