The atomic-state quantum teleportation in a dissipative environment is investigated by the quantum theory of damping - density operator approach and the numerical calculations. The effects of fidelity for different initial atomic-states are discussed. The results show that, when only the input atomic-state is exposed to the squeezed vacuum reservoirs, the fidelity of atomic-state with larger probability in the ground state is larger than that of other state; on the other hand, when the quantum channel is exposed to the reservoirs, the input state with equal probability in the ground state and the excited state has the largest fidelity in all the teleported states.