Secure Sockets Layer (SSL) and Transport Layer Security (TLS) protocols facilitates a secure framework for identity authentication, data encryption, and message integrity verification. However, with the recent development in quantum computing technology, the security of conventional key-based SSL/TLS protocols faces vulnerabilities. In this paper, we propose a scheme by integrating the quantum key into the SSL/TLS framework. Furthermore, the application of post-quantum algorithms is used to enhance and complement the existing encryption suites. Experimental results show that the proposed SSL/TLS communication system based on quantum keys exhibits high performance in latency and throughput. Moreover, the proposed system showcases good resilience against quantum attacks.