We introduce a new notion of Reeb invariant structure Jacobi operator and two kinds of singular normal vector field N for a real hypersurface M in the complex quadric Q m , m ≥ 3. If the unit normal N is A-isotropic, we give a classification of Hopf real hypersurfaces with Reeb invariant structure Jacobi operator in the complex quadric Q m , for m ≥ 3