This Project presents a new scheme for asymmetric bidirectional controlled quantum teleportation (ABCQT) protocol of two- and three-qubit unknown states. In the protocol, Alice intends to transmit an unknown two-qubit entangled state to Bob, and Bob needs to transmit an unknown three-qubit entangled state to Alice under the supervision of Charlie, who is the controller of the protocol. In order to establish the teleportation protocol, an eight-qubit cluster state is used as the quantum channel. States are teleported over the channel by using GHZ-state measurements and applying a proper unitary transformation. With this method, the communication purpose is realized more advantageous compared to recently presented protocols. Furthermore, the quantum circuit of the protocol is simulated using IBMQ qasm_simulator and Qiskit library, and the validation of the protocol is shown. The quantum circuit for realizing the proposed asymmetric bidirectional controlled quantum teleportation (ABCQT) protocol. The circuit consists of five different sections: I. Alice and Bob prepare their pure states II. The quantum channel is created and shared among parties III. Alice and Bob carry out GHZ-measurements, and Charlie also performs a single-qubit measurement in X basis IV. Bob applies an appropriate unitary function on his state based on Alice and Charlie’s measurements outcomes V. Alice applies an appropriate unitary function based on Bob’s measurement results.