We propose a protocol of asymmetric controlled bidirectional quantum teleportation of two- and three-qubit states. That is to say, Alice wants to teleport an arbitrary two-qubit state to Bob, and Bob wants to teleport an arbitrary three-qubit state for Alice via the control of supervisor Charlie. By using the eleven-qubit entangled state as the quantum channel, Alice can teleport an arbitrary two-qubit state for Bob and Bob can teleport an arbitrary three-qubit state for Alice simultaneously. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.