In　this　paper,　we　shall　firstly　illustrate　why　we　should　introduce　set-valued　stochastic　integrals,　and　then　we　shall　discuss　some　properties　of　set-valued　stochastic　processes　and　the　relation　between　a　set-valued　stochastic　process　and　its　selection　set.　After　recalling　the　Aumann　type　definition　of　stochastic　integral,　we　shall　introduce　a　new　definition　of　Lebesgue　integral　of　a　set-valued　stochastic　process　with　respect　to　the　time　t.　Finally　we　shall　prove　the　presentation　theorem　of　set-valued　stochastic　integral　and　discuss　further　properties　that　will　be　useful　to　study　set-valued　stochastic　differential　equations　with　their　applications.