In　this　paper,　we　firstly　introduce　the　concept　of　set-valued　square　integrable　martingales.　Secondly,　we　give　the　definition　of　stochastic　integral　of　a　stochastic　process　with　respect　to　a　set-valued　square　integrable　martingale,　and　then　prove　the　representation　theorem　of　this　kind　of　integral　processes.　Finally,　we　show　that　the　stochastic　integral　process　is　a　set-valued　sub-martingale.　©　2010　Springer-Verlag　Berlin　Heidelberg.