3D animation of conversational agents becomes popular in our daily life such as Samsung's Neon. Eye movement of the agent is sometimes more important non-verbal information than words to share what they think and how they feel in face-to-face conversation. To smooth and sustain human-agent conversation, we propose a method to generate natural eye movements by modeling each state of conversation based on analysis of eye-tracking data. We acquired human eye movements in different states with eye tracker system to build a finite automaton. As a result, our method generates realistic eye movements by switching states in the finite automaton according to specified state of conversation.