As a pivotal virtualization technology, the network digital twin (DT) is expected to accurately reflect real-time status and abstract features in the ongoing sixth generation (6G) networks. In this article, we propose an artificial intelligence (AI)-native network DT framework for 6G networks to enable the synergy of AI and network DT, thereby facilitating intelligent network management. In the proposed framework, AI models are utilized to establish network DT models to support network status prediction, network pattern abstraction, and network management decision-making. Furthermore, potential solutions are proposed to enhance the performance of network DT. Finally, a case study is presented, followed by a discussion of open research issues that are essential for the AI-native network DT in 6G networks.