The dynamic evolution of the average fidelity of quantum teleportation is investigated using quantum-state-diffusion (QSD) theory when two interacting qubits strongly coupled to a bosonic bath. The effects of environmental memory, anisotropic coupling parameters, Dzyaloshinskii-Moriya (DM) interaction and external magnetic field on quantum teleportation are analyzed and discussed. Results show that the memory effect of the environment can effectivelyimprove the average fidelity. When the quantum channel is maximum entangled state, the optimal average fidelity can be obtained by increasing the coupling parameters, DM interaction or the external magnetic field. However, when the quantum channel is changed, the effect of the coupling constant between qubits on average fidelity is opposite. It indicates that the combination of the non-Markovian memory effect and optimal parameter can be used to achieve ideal quantum teleportation in theory.