The　purpose　of　this　study　is　to　evaluate　the　influence　of　soil　spatial　variability　(SSV)　on　the　simulation　of　depth　varying　multi-support　seismic　motions　(DMSMs)　at　offshore　sites.　Firstly,　the　random　field　theory　is　used　to　quantify　the　extent　of　SSV,　and　a　series　of　random　field　models　with　different　characteristics　are　established　for　an　offshore　site　by　changing　the　coefficient　of　variation　(COV)　and　correlation　distance　of　soil　parameters.　Then,　the　simulation　approach　for　random　ground　motion　transfer　functions　(GMTFs)　and　DMSMs　at　offshore　sites　are　introduced.　The　sensitivity　of　each　uncertain　soil　parameter　on　the　offshore　seismic　motions　is　explored　using　the　single　variable　method.　Finally,　the　effects　of　SSV　on　the　GMTFs　and　DMSMs　are　investigated,　in　which　the　effects　of　COV　and　correlation　distance　are　studied　in　detail.　The　results　demonstrate　that　SSV　has　a　remarkable　influence　on　the　GMTFs　of　offshore　sites,　which　results　in　a　large　intensity　variation　of　DMSMs.　The　sensitivity　analysis　indicates　that　the　soil　density　and　shear　modulus　are　influential　factors　for　the　horizontal　components　of　DMSMs;　except　these　two　parameters,　the　Poisson＇s　ratio　also　significantly　affects　the　vertical　DMSMs.　Moreover,　both　COV　and　correlation　distance　can　lead　to　certain　variability　in　the　GMTFs　and　DMSMs,　and　the　effect　of　COV　is　more　prominent　than　the　correlation　distance.　This　study　provides　an　effective　approach　for　the　simulation　of　DMSMs　at　random　offshore　sites,　which　is　valuable　for　rational　probabilistic　seismic　performance　assessment　of　offshore　engineering　structures.