Finite-time　stability　means　that　the　trajectory　of　dynamical　system　converges　to　a　Lyapunov　stable　equilibrium　state　in　finite　time.　The　finite　time　stabilization　of　traffic　flow　model　can　improve　the　transportation　efficiency　and　reduce　the　occurrence　of　traffic　congestion.　In　this　letter,　the　finite-time　boundary　stabilization　problem　for　the　Lighthill-Whitham-Richards　(LWR)　traffic　flow　model　is　considered,　in　which　a　variable　speed　limit　(VSL)　device　is　applied　at　the　downstream　boundary　and　a　finite-time　boundary　controller　is　designed　to　drive　the　traffic　density　to　the　steady　state　in　finite　time.　By　utilizing　the　method　of　characteristics　to　illustrate　the　property　of　finite-time　convergence　and　the　Lyapunov　function　approach　to　prove　stability,　the　local　finite-time　stability　of　LWR　traffic　flow　system　is　ensured　in　$H^{2}$　-norm.　Moreover,　the　settling-time　can　be　given　depended　on　the　initial　value　and　the　parameters　of　finite-time　boundary　controller.　Lastly,　a　numerical　simulation　example　is　presented　to　verify　the　effectiveness　of　the　theoretical　results.　©　2017　IEEE.