Teleportation schemes with a tripartite entangled state in cavity QED are investigated. The schemes do not need Bell state measurements and the successful probabilities reach optimality. In addition, the schemes are insensitive to both the cavity decay and the thermal field. We first consider two teleportation schemes via a tripartite GHZ state. The first one is a controlled one for an unknown single-qubit state. The second scheme is teleportation of unknown two-atom entangled state. Then we consider teleporting of single-qubit arbitrary state via a tripartite W state.