This paper investigates a transmission scheme for enhancing quantum communication security, aimed at improving the security of space-air-ground integrated networks (SAGIN). Quantum teleportation achieves the transmission of quantum states through quantum channels. In simple terms, an unknown quantum state at one location can be reconstructed on a particle at another location. By combining classical Turbo coding with quantum Shor error-correcting codes, we propose a practical solution that ensures secure information transmission even in the presence of errors in both classical and quantum channels. To provide absolute security under SAGIN, we add a quantum secure direct communication (QSDC) protocol to the current system. Specifically, by accounting for the practical scenario of eavesdropping in quantum channels, the QSDC protocol utilizes virtual entangled pairs to detect the presence of eavesdroppers. Consequently, the overall scheme guarantees both the reliability and absolute security of communication.