The author computes the Betti number of the moduli space of rank three stable Higgs bundles on a Riemann surface. A Higgs bundle is a pair \((E,\varphi)\), where \(E\) is a vector bundle and \(\varphi \in \operatorname{Hom} (E,E \otimes K)\) that satisfies certain stability condition. The computation is a generalization of Hitchin’s computation of rank two case. It exploits the fact that the moduli space admits a circle action which respects the symplectic form of the moduli space, and the moment map is a perfect Morse function. Hence the computation can effectively be reduced to a detailed study of the critical set of the moment map, which is the fixed point set of the circle action. It turns out that the fixed points of the circle action are decomposable pairs \((E, \varphi)\). The main part of the paper is devoted to analyse such decomposition and the geometry of the critical set. The rank three condition is used so that the structure of the critical set can be described completeley.