Quantum teleportation via the entangled channel composed of a two-qubit Heisenberg XYZ model with Dzyaloshinski-Moriya (DM) interaction in the presence of intrinsic decoherenee has been investigated. We find that the initial state of the channel plays an important role in the teleported state and the average fidelity of teleportation. When the initial channel is in the state [ψ1(0)>=a|00> + b|11>, the average fidelity is equal to 1/3 constantly, which is independent of the DM interaction and the intrinsic decoherence effect. But when the channel is initially in the state [ψ2(0)> = c|01) + d|10>, the average fidelity is always larger than 2/3. Moreover, under a certain condition, the average fidelity can be enhanced by adjusting the DM interaction, and the intrinsic decoherence leads to a suppression of the fluctuation of the average fidelity.