We present a scheme of atomic-state teleportation by using a quantum switch (QS). Based on the principle of QS and the quantum interference effect, a controlled-NOT operation between atom and cavity is proposed and used to transform the joint measurement of the von Neumann type into the discrete measurements. A detection method using several atoms resonantly interacting with field state is also presented to read out the field state in a cavity. The fidelity due to cavity dissipation is discussed. In our scheme, since the transfer of quantum information between atom and cavity is achieved by nonresonant atom-cavity interaction, three-bit classical information is transmitted from Alice to Bob to complete teleportation.