In　this　paper,　by　using　qualitative　analysis,　we　investigate　the　number　of　limit　cycles　of　perturbed　cubic　Hamiltonian　system　with　perturbation　in　the　form　of　(2n　+　2m)　or　(2n　+　2m　+　1)th　degree　polynomials.　We　show　that　the　perturbed　systems　has　at　most　(n　+　m)　limit　cycles,　and　has　at　most　n　limit　cycles　if　m　=　1.　If　m　=　1,　n　=　1　and　m　=　1,　n　=　2,　the　general　conditions　for　the　number　of　existing　limit　cycles　and　the　stability　of　the　limit　cycles　will　be　established,　respectively.　Such　conditions　depend　on　the　coefficients　of　the　perturbed　terms.　In　order　to　illustrate　our　results,　two　numerical　examples　on　the　location　and　stability　of　the　limit　cycles　are　given.　(c)　2006　Elsevier　Ltd.　All　rights　reserved.