<p>The booming of artificial intelligence (AI) agents has brought about promising business scenarios for sixth-generation (6G) mobile networks, while simultaneously posing significant challenges to network functionalities and infrastructure. These AI agents can be deployed on end devices (e.g., intelligent robots and intelligent cars) or as digital entities (e.g., personal AI assistants). As novel service entities with autonomous decision-making and task execution capabilities, AI agents introduce potential risks of uncontrollable actions and privacy disclosures. AI agents also require new 6G capabilities beyond traditional communication, including multimodality information interaction (e.g., AI models and tokens) and support for service requirements (e.g., computing and sensing of data). In this article, we introduce the concept of AI-agent communication network (ACN), a new paradigm to enable global information interaction and on-demand capability provisioning for single or multiple AI agents. We first introduce the vision and architectural framework of ACN. Then, key technologies and future research directions related to ACN are discussed. Furthermore, we provide potential use cases to elaborate on how ACN can expand the service capabilities of 6G networks.</p>