We investigate the characteristics of entanglement teleportation of a two-qubit and three-qubit Heisenberg XYZ model under different Dzyaloshinskii---Moriya (DM) interactions with intrinsic decoherence taken into account. The two-qubit results reveal that the dynamics of entanglement is a symmetric function about the coupling coefficient $$J$$J for the $$z$$z-component DM system, whereas it is not for the $$x$$x-component DM system. The ferromagnetic case is superior to the antiferromagnetic case to restrain decoherence when using the $$x$$x-component DM system. The dependencies of entanglement, the output entanglement, and the average fidelity on initial state angle $$\alpha $$? all demonstrate periodicity. Moreover, the $$x$$x-component DM system can get a high fidelity both in two-qubit and in three-qubit teleportation protocol.