We have searched for the lepton-flavor-violating decays τ- decays into ℓ-KS 0 and ℓ-KS 0KS 0 (ℓ=e or μ), using a data sample of 671 fb-1 collected with the Belle detector at the KEKB asymmetric-energy e+e- collider. No evidence for a signal was found in any of the decay modes, and we set the following upper limits for the branching fractions: B(τ-→e-KS 0)<2.6 ×10-8, B(τ-→μ-KS 0)<2 .3×10-8, B(τ-→e-KS 0KS 0)<7.1×10-8 and B(τ-→μ-KS 0 KS 0)<8.0×10-8 at the 90% confidence level. © 2010 Elsevier B.V.