A Stone space is a zero dimensional, compact and T0 topological space. Also it is called Boolean space. There are a lot of methods for obtainnig compact space. Aleksandrov, Stone-Cech, Wallman and Fan-Gottesman compactification are four of them. In this paper, it is discussed Fan-Gottesman compactification of regular space with normal base and necessary and sufficient conditions for Fan-Gottesman compactification of T3 space to be a Stone space are given by considering relation between the Stone space and compact space.