Integrated　Sensing　and　Communication　(ISAC)　Systems,　which　can　support　simultaneous　information　transmission　and　target　detection,　have　been　regarded　as　promising　solutions　for　various　emerging　wireless　network　applications.　In　this　work,　a　covert　transmission　system　with　the　aid　of　the　ISAC　technique　is　proposed,　where　the　radar　intends　to　sense　a　target　and　send　message　to　legitimate　users　covertly　against　the　warden's　surveillance　with　either　perfect　or　imperfect　channel　state　information　(CSI)　at　the　warden.　We　formulate　a　beamforming　optimization　problem　for　the　dual-function　signal　used　for　sensing　and　communication　to　maximize　the　covert　throughput,　subject　to　a　covertness　constraint,　a　maximum　transmit　power　constraint,　and　a　radar　detection　constraint.　We　then　determine　the　sufficient　conditions　under　which　the　covert　beamforming　design　problem　can　be　solved　by　semidefinite　relaxation　(SDR).　Numerical　results　show　that　the　proposed　covert　ISAC　system　can　guarantee　covert　transmission　while　ensuring　a　certain　level　of　sensing　performance,　and　there　exists　a　performance　trade-off　between　the　considered　radar　detection　and　covert　transmission.　IEEE