Continuous-variable quantum remote state teleportation plays an important role in constructing continuous-variable quantum computing and quantum information networks. In practical communication processes, quantumentanglement typically interacts with the surrounding environment due to environmental interference, resulting in a reduction of entanglement and consequently affecting the correct transmission of quantum information, leading to a decrease in the fidelity of teleportation. A practical communication system is a more complex network than a simple point-to-point connection. Therefore, it is necessary to use multipartite entangled light fields to establish complex quantum networks. In this paper, a quantum teleportation network based on four-mode GHZ entangled light fields is constructed. The fidelity formula for transmitting quantum states in this network system is derived, and simulation results show the relationship between the fidelity and the gain factor under different compression parameters. The simulations indicate that for a given compression parameter, there exists an optimal gain factor that maximizes the fidelity. The fidelity initially increases and then decreases as the gain factor increases. A larger compression parameter results in better fidelity recovery of the quantum state. However, even with a large compression parameter, the fidelity cannot reach high values if the gain factor is not properly chosen. By increasing the compression parameter r and selecting the appropriate gain factor, the fidelity can be improved. However, in the actual system, factors such as optical device loss, noise and detector performance need considering comprehensively to achieve the best transmission and detection efficiency to achieve higher fidelity. In the design and experiment, it is necessary to comprehensively consider the transmission efficiency and detection efficiency to optimize the system parameters to achieve higher fidelity. Ideally, when the squeezing parameter r approaches infinity and the gain factor achieves the optimal value, the quantum correlation between the four sub-modes satisfies that the input state is equal to the output state, that is, the input state and the output state are completely consistent.The multi-component entangled state provides more resources, which help achieve more complex communication tasks. It can expand the communication channels and transmission capabilities of quantum teleportation and achieve higher-level secure communication. The results emphasize the importance of transmission efficiency and detection efficiency in quantum teleportation, which provide key factors and strategies for optimizing fidelity. It is of guiding significance for realizing high-fidelity quantum teleportation.