A new method which employs a mixed-valence cluster of M.sub.y.sup.z+ [Fe(II)(CN).sub.6 ] coated on an electrode surface to determine hydrogen peroxide concentration electrochemically is developed. M of the mixed-valence compound can be Co, Ni, Cr, Sc, V, Cu, Mn, Ag, Eu, Cd, Zn, Ru or Rh; z is the valence state of M; and y=4/z. In addition, this invention also reveals a new approach to determine a concentration of a hydrogen peroxide precursor, wherein a catalyst is immobilized in the matrix or on the surface of the mixed-valence compound on the electrode. In a typical biochemical system, the catalyst can be a glucose oxidase and blood sugar is catalyzed to form hydrogen peroxide.