Let M be a real hypersurface of a complex space form with almost contact metric structure (φ,ξ,η,g). In this paper, we prove that if the structure Jacobi operator R_ξ=(·,ξ) ξ is φ▽_ξξ-parallel and R_ξ commute with the shape operator, then M is a Hopf hypersurface. Further, if R_ξ is φ▽_ξξ-parallel and R_ξ commute with the Ricci tensor, then M is also a Hopf hypersurface provided that TrR_ξ is constant.