The　electron　transport　of　a　system　consisting　of　a　Kondo　dot　and　two　Luttinger　liquid　(LL)　leads　is　theoretically　studied　by　use　of　nonequilibrium　Green　function　approach.　In　the　Kondo　regime,　the　zero　bias　anomaly　appears　and　the　density　of　states　of　the　dot　obeys　a　power-law　scaling　at　positive　energy　part　with　an　exponent　beta/2　=　1/g　-　1,　where　g　reflects　the　electron　interaction　in　the　LL　leads.　The　differential　conductance　shows　a　power-law　scaling　both　in　bias　voltage　and　in　temperature,　with　the　exponent　being　beta.　The　power-law　temperature　dependence　of　the　peak　conductance　is　observed　in　different　temperature　regimes.　These　features　are　ascribed　to　the　LL　correlation　in　the　leads.　Our　work　describes　both　the　zero　bias　anomaly　and　power-law　scalings　within　one　theoretical　frame.