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 ...