We search for the neutrinoless, lepton-flavor-violating tau decays tau- -->l-}V0, where l is an electron or muon and V0 is a vector meson reconstructed as phi-->K+K-, rho-->pi+pi-, K-->K+pi-, K[over ]-->K-pi+. The analysis has been performed using 451 fb-1 of data collected at an e+e- center-of-mass energy near 10.58 GeV with the BABAR detector at the PEP-II storage rings. The number of events found in the data is compatible with the background expectation, and upper limits on the branching fractions are set in the range (2.6-19)x10-8 at the 90% confidence level.