Based　upon　the　force-bearing　characteristics,　the　combined　finite　element　model　of　beam　elements,　truss　elements　and　cable　elements　is　selected,　and　an　incremental-iterative　nonlinear　finite　element　technique　is　developed　to　analyse　the　dynamic　response　of　the　long　span　hybrid　spatial　structure　of　cable-supported　lattice　shells.　The　seismic　analysis　is　carried　out　by　step-by-step　method　in　the　time　domain　with　inputting　the　three-dimensional　earthquake　ground　motion　for　a　K8　type　cable-supported　lattice　shell.　The　results　indicate　that　the　structure　has　a　good　seismic　performance.　In　addition,　the　rules　of　seismic　response　are　systematically　studied　by　means　of　changing　the　main　parameters　of　the　structure.　Finally　the　conclusion　is　drawn　that　the　rise-span　ratio　and　the　lengths　of　bars　are　the　main　control　parameters　for　seismic　design.