As a typical cross-chain technology, the relay chain is widely applied. The transaction security in the cross-chain application of a traditional relay chain depends on the reliability of the relay part, which relies on the autonomous performance of the relay chain. However, this will lead to the risk of trust breach. There are three main security concerns: 1) No security access control for authentication; 2) Consensus transmission depends on the authority of the relay node; 3) Potential security threats from quantum computing attacks. To tackle these issues, a quantum cross-chain model (QCC) is proposed to provide post-quantum security. The QCC offers an access control policy for the global identity of application chains and two-way authentication for the cross-chain network, and a secure solution that deploys a quantum ring signature scheme (QRS) provided with audit and key-loss security for cross-chain transactions, contributing to decentralization, reliability, consensus transmissionand security of the relay chain. From a system security perspective, the security of QCC is enhanced by the underlying cryptographic algorithm--QRS, eliminating under-layer attacks and bringing a stronger guarantee for the security and scalability of upper-layer applications. In addition, the model has the advantage of scalability and supports multi-party transactions.