By　using　means　of　density　functional　theory　calculations,　we　reported　the　heterostructure　consisting　of　monolayer　MoSSe　and　graphene,　as　a　promising　anode　material　for　lithium　ion　batteries.　We　investigated　the　adsorption　and　diffusion　of　lithium　atoms　in　the　MoSSe　and　MoSSe_graphene　heterostructures,　and　we　found　that　the　combination　with　graphene　makes　the　lithium　atoms＇　adsorption　more　stable,　meanwhile,　the　diffusion　barriers　on　the　surface　are　lower　than　that　at　the　interface,　which　are　comparable　to　the　barriers　on　the　corresponding　monolayers.　The　maximum　lithium　storage　capacity　of　the　heterostructure　is　enhanced　to　390　mAh/g.　Our　work　made　a　comparison　with　all　the　typical　structures　of　MoSSe　and　MoSSe_graphene,　and　suggests　that　the　S　side　of　MoSSe-2　combined　with　graphene　and　the　Se　side　of　MoSSe-2　combined　with　graphene　are　the　promising　materials　for　their　higher　lithium　capacity　and　charge/discharge　rates.