In this paper, we study carefully the quantum teleportation by means of a channel of a three-qubit Heisenberg XXZ ring, and calculate the fidelity of quantum teleportation. Comparing the four XXZ models: one without three-site interaction, one with XZX +YZY type three-site interaction, one with XZY-YZX type three-site interaction, one with both the two kinds of the three-site interaction, we find some ideal models by which the teleportation only needs a weakest magnetic field and a highest temperature to work successfully. The result could provide a theoretical basis for later experiments.