The　joint　effects　of　the　electron-phonon　interaction　and　Kondo　effect　on　the　charge　and　heat　transport　through　a　single　molecule　transistor　are　investigated　by　applying　the　improved　canonical　transformation　and　noncrossing　approximation　technique.　We　find　that　the　electron-phonon　interaction　decreases　the　conductance,　thermopower　and　the　Wiedemann-Franz　law　in　the　Kondo　regime　due　to　the　splitting　and　the　decreasing　of　the　main　Kondo　peak.　However,　the　thermoelectric　figure　of　merit　achieves　enhancement　with　the　electron-phonon　coupling　strength　increasing.　In　addition,　the　dip　value　of　the　thermopower　at　the　Kondo　temperature　for　the　different　electron-phonon　coupling　strength　can　give　a　straightforward　reliable　estimate　of　the　electron-phonon　coupling　strength.　(C)　2010　Elsevier　B.V.　All　rights　reserved.