With a large number of news available on the internet everyday, it is an interesting work to automatically organize news events by time order and dependencies between events. The work may help users to conveniently and quickly browse news event evolution. This paper defines an Event Timeline Analysis (ETA) task to meet the need. Compared with existing works, ETA presents event evolution in graph manner, and incrementally updates the process of events evolving so as to better fit feature of stream of news on the internet. In order to complete ETA task, this paper proposes an Event Evolving Graph (EEG) structure and building and tidying algorithm of EEG. Experiments demonstrate the utility and feasibility of the method.