Quantum controlled teleportation is the transmission of the quantum state under the supervision of a third party. This paper presents a theoretical and experimental combination of an arbitrary two-qubit quantum controlled teleportation scheme. In the scheme, the sender Alice only needs to perform two Bell state measurements, and the receiver Bob can perform the appropriate unitary operation to reconstruct arbitrary two-qubit states under the control of the supervisor Charlie. We verified the operation process of the scheme on the IBM Quantum Experience platform and further checked the accuracy of the transmitted quantum state by performing quantum state tomography. Meanwhile, good fidelity is obtained by calculating the theoretical density matrix and the experimental density matrix. We also introduced a sequence of photonic states to analyze the possible intercept-replace-resend, intercept-measure-resend, and entanglement-measure-resend attacks on this scheme. The results proved that our scheme is highly secure.