For　extremely　high　field　magnets,　the　low-temperature　superconducting/high-temperature　superconducting　(LTS/HTS)　structure　is　an　efficient　and　economical　solution.　In　an　LTS/HTS　magnet　system,　the　LTS　background　field　magnet　is　deeply　mutual　inductance　coupled　with　the　HTS　insert　magnet.　A　sudden　background　LTS　magnet　quench　may　potentially　destroy　the　double　pancakes　(DPs)　of　the　insert　HTS　magnet　because　of　the　induced　current　and　the　resulting　additional　electromagnetic　stress.　To　improve　the　safety　and　stability　of　the　LTS/HTS　magnet　system,　this　article　proposed　a　new　passive　protecting　scheme　of　the　LTS/HTS　system.　In　this　scheme,　a　magnetic　dam　is　arranged　between　the　insert　magnet　and　the　background　field　magnet.　When　the　background　field　magnet　quenches,　the　magnetic　dam　can　help　to　slow　down　the　magnetic　flux　variation　in　the　insert　magnet.　According　to　the　simulation　results,　a　magnetic　dam　can　significantly　reduce　the　instantaneous　stress　rise　of　the　insert　magnet　by　65.3%.　The　protective　effect　of　the　magnetic　dam　was　also　verified　by　the　experiments　with　a　Bi-2223　insulating　coil　magnet.　The　structural　parameters　affecting　the　isolating　effect　of　the　magnetic　dam　were　also　discussed.　Based　on　this　work,　researchers　can　further　improve　the　safety　and　stability　of　the　LTS/HTS　magnet　system.