We　study　the　shot　noise　of　a　strongly　correlated　quantum　dot　weakly　coupled　to　Luttinger　liquid　leads　in　the　Kondo　regime　by　means　of　the　extended　equation　of　motion　method.　A　general　zero-frequency　shot　noise　formula　with　good　convergence　is　derived.　The　shot　noise　exhibits　a　non-monotonic　dependence　on　voltage　for　weak　intralead　interaction.　There　is　a　peak　around　the　Kondo　temperature　at　low　voltage　when　the　interaction　is　very　weak,　and　its　height　decreases　rapidly　with　the　intralead　interaction　increasing.　When　the　interaction　is　moderately　strong　the　peak　disappears　and　the　shot　noise　scales　as　a　power　law　in　bias　voltage,　indicating　that　the　intralead　electron　interaction　suppresses　the　shot　noise.　It　is　possible　that　the　measurements　of　the　shot　noise　spectrum　can　extract　the　information　of　the　intralead　interaction.　(C)　2014　Elsevier　B.V.　All　rights　reserved.