Abstract: To suppress the decoherence effects caused by amplitude damping noise in the channel on the distribution of maximally entangled states, and to achieve faithful transmission of unknown quantum states in quantum teleportation and multi-party quantum state sharing schemes, this paper proposes an entanglement compensation method. This method involves cyclically transmitting a single qubit from the maximally entangled Bell state through an amplitude damping channel, performing controlled-NOT gates, specific joint unitary operations, and single-qubit measurements, ultimately achieving entanglement compensation for the quantum system. Building on this, this paper proposes a scheme for sharing maximally entangled Bell and GHZ states in the amplitude damping channel, with verification by Qiskit simulations. Mathematical derivations demonstrate that the proposed method can enable the sharing of four maximally entangled Bell states and four maximally entangled GHZ states in the amplitude damping channel. Simulation analysis results based on the Qiskit platform indicate that the success rate of this scheme gradually decreases as the amplitude damping strength in the channel increases and the number of participants grows.