The dynamic evolution of the fidelity of quantum teleportation in a single three-level atom coupled to a multi-mode non-Markovian bosonic environment is studied by using the quantum state diffusion method, and the effects of different parameters on the fidelity are analyzed. The results show that when the three-level atom is coupled with the strong non-Markovian environment, and the initial state of the three-level atom is in excited state or metastable state, the fidelity of quantum teleportation of three-level atoms has long relaxation time and good robustness. In addition, the external magnetic field is used to control the quantum teleportation of the three-level atom, which can make the three-level atom have a fidelity with good robustness.