In　this　paper,　we　shall　firstly　illustrate　why　we　should　consider　integral　of　a　stochastic　process　with　respect　to　a　set-valued　square　integrable　martingale.　Secondly,　we　shall　prove　the　representation　theorem　of　set-valued　square　integrable　martingale.　Thirdly,　we　shall　give　the　definition　of　stochastic　integral　of　a　stochastic　process　with　respect　to　a　set-valued　square　integrable　martingale　and　the　representation　theorem　of　this　kind　of　integrals.　Finally,　we　shall　prove　that　the　stochastic　integral　is　a　set-valued　sub-martingale.　(C)　2010　Elsevier　Inc.　All　rights　reserved.