Quantum network routing algorithm is important for large-scale quantum network, especially when long-distance quantum communication system is established. In this paper, a quantum grid network model based on Trusted Center is proposed. With two-way quantum communication, the original information does not need to be transmitted through the quantum relay node, but instead a quantum entanglement channel established by two remote users using quantum teleportation. Using this model, the security of quantum relay nodes and quantum information transmission channels can be effectively guaranteed. Upon this, a quantum network routing algorithm is proposed to further improve the performance. When users need to set up an m-path quantum communication in the quantum grid network, this algorithm can greatly improve the efficiency of quantum communication, accompanied with self-correcting ability. Security analysis proves that the proposed m-path routing algorithm can greatly improve the security probability of quantum communication in quantum network.