With the continuous progress of mobile communication technology and the continuous growth of network demand, the network structure is becoming increasingly complex. However, traditional network management is difficult to meet the needs of future development. In the future, intelligent autonomous networks could perform flexibly and efficiently with the help of AI-driven automated analysis and multidimensional data perception. Still, at the same time, this also requires a more intelligent approach to network management. The large language models (LLMs) represented by generative pre-trained transformer (GPT) will play an important role in promoting intelligent autonomy of communication networks. Therefore, this paper studies the specific methods of GPT promoting intelligent autonomy of communication networks, and analyzes how GPT enables intelligent autonomy in communication networks from different perspectives. Specifically, it includes GPT-assisted base station site selection, antenna design optimization and virtualized intelligent slicing, as well as network operations and maintenance from anomaly detection to automatic recovery, and network traffic optimization, coverage optimization and signaling tracing. Finally, we also propose some challenges, such as the inconsistent quality of training data sets, insufficient computing resources, and high risks to network privacy and security. We also propose some corresponding solutions and predict future development trends.