In　this　paper,　we　consider　consensus　problem　for　a　class　of　nonlinear　multi-agents　system.　The　interaction　topology　among　the　agents　is　assumed　to　be　fixed　and　directed　topology.　To　achieve　the　consensus　problem,　a　neighbor-based　nonlinear　state　feedback　controller　is　designed　for　each　agent,　based　on　algebraic　graph　and　the　positive　polynomial　theories.　A　sufficient　condition　is　established　to　solve　consensus　problem　of　the　considered　nonlinear　multi-agents　systems.　Then,　the　state　feedback　gain　matrix　can　be　obtained　from　the　feasible　solution　to　the　sum　of　squares　programs.　Finally,　a　simulation　example　is　given　to　illustrate　our　approach.　©　2019　IEEE.