We construct an entangled quantum heat engine based on two-coupled-qubit XXZ model with Dzyaloshinski-Mariya interaction. The work done and the heat transfer are discussed according to the definition first given by Kieu, The relations between the entanglement and heat transfer, work output and efficiency are analyzed for different anisotropic parameters. The results show that the second law of thermodynamics holds in entangled systems and the isolines for the efficiency are looped curves. When the anisotropic parameter Δ is small enough, the heat engine can operate in both C1 > C2 and C1C2, however, when Δ is large, the heat engine operates in C1 > C2 only.