This paper deals with an even dimensional simply connected compact Riemannian manifold \(M\) with strictly positive sectional curvature. Let \(G\) be a compact Lie group acting by isometries on \(M\) with a codimension one orbit. Then, it is well-known that \(M\) is called a cohomogeneity one \(G\)-manifold.
In this paper, the author has proved the following main result: If \(G\) is a compact semisimple (but not simple) Lie group, then the cohomogeniety one \(G\)-manifold \(M\) is equivariantly diffeomorphic to a compact rank one symmetric space.