In the paper,taking the atomic EPR entanglement states as quantum channel,we investigate the fidelityof quantum teleportation of atomic state in thermal environment and vacuum reservoir by means of quantum theory ofdamping-density operator approach,and the average fidelities are calculated.the results show that the atomic quantumchannel state |φ〉= (l/2)(|00〉 + |11〉) is more robust than |φ〉= (l/2)(|01〉+ |10〉) in teleportation process whenthey are subject to the dissipative environments.