The　joint　effects　of　the　electron-phonon　interaction　and　electron-electron　interaction　in　the　Luttinger　liquid　leads　on　nonequilibrium　transport　through　a　single-molecule　transistor　in　the　Kondo　regime　are　investigated　by　using　the　improved　canonical　transformation　scheme　and　equation　of　motion　approach.　For　weak　intralead　electron　interaction,　a　pronounced　dip　around　zero　bias,　accompanied　by　a　series　of　discrete　single-electron　tunneling　peaks　is　observed　in　the　differential　conductance.　With　the　increase　of　the　intralead　interaction,　the　phonon-assisted　peaks　turn　into　dips,　which　demonstrates　a　phonon-assisted　two-channel　Kondo　physics.　For　a　certain　region　of　interaction　strength　the　inelastic　electron　tunneling　can　dominate　electron　transport.　Our　results　well　explain　the　experiments　of　zero　bias　anomaly.　(C)　2013　Elsevier　B.V.　All　rights　reserved.