A　time-domain　explicit　finite　element　method　for　the　elastic　wave　propagation　of　transversely　isotropic　fluid-saturated　porous　media　is　put　forward.　The　space　decoupling　technology　is　adopted　for　the　space　discretization　and　the　time-domain　explicit　step-by-step　calculating　format　for　the　time　discretization.　Using　the　method,　the　dynamic　response　of　transversely　isotropic　fluid-saturated　porous　media　is　calculated　and　analyzed,　and　the　calculated　results　are　compared　with　those　of　isotropic　fluid-saturated　porous　media.　The　effect　of　the　value　of　anisotropic　coefficient　on　the　calculated　results　of　the　dynamic　response　of　transversely　isotropic　fluid-saturated　porous　media　is　also　studied.　The　calculated　results　show　that　the　dynamic　response　of　transversely　isotropic　fluid-saturated　porous　media　has　remarkable　difference　from　that　of　isotropic　fluid-saturated　porous　media,　and　the　value　of　anisotropic　coefficient　has　a　significant　effect　on　the　calculated　results　of　the　dynamic　response　of　transversely　isotropic　fluid-saturated　porous　media.　Meanwhile,　the　present　numerical　calculation　indicates　that　the　time-domain　explicit　finite　element　method　is　effective　for　the　calculation　and　analysis　of　the　dynamic　response　of　transversely　isotropic　fluid-saturated　porous　media.