Let M be a real hypersurface with almost contact metric structure $(phi,;xi,;eta,;g)$ in a nonflat complex space form $M_n(c)$. In this paper, we prove that if the structure Jacobi operator $R_xi$ commutes with both the structure tensor $phi$ and the Ricc tensor S, then M is a Hopf hypersurface in $M_n(c)$ provided that the mean curvature of M is constant or $g(Sxi,;xi)$ is constant.