Requirements changes frequently occur at any time of a software development process, and their management is a crucial issue to develop software of high quality. Meanwhile, goal-oriented analysis techniques are being put into practice to elicit requirements. In this situation, the change management of goal graphs and its support are necessary. This paper presents a technique related to the change management of goal graphs, realizing impact analysis on a goal graph when its modifications occur. Our impact analysis detects conflicts that arise when a new goal is added, and investigates the achievability of the other goals when an existing goal is deleted. We have implemented a supporting tool for automating the analysis. Two case studies suggested the efficiency of the proposed approach.