Abstract Non-resonant X-ray diffraction measurements have been made on a dense Kondo material CeB 6 . A series of (n, n, n) reflections with n =half integers has been observed in phase III of this compound. The magnetic field dependence of these reflections at 1.6 K as well as the temperature dependence in zero field have been measured. The intensity of these reflections shows anomaly at the phase boundaries determined by Effantin and coworkers. From these experimental observations, we argue that the (n, n, n) reflections reflect an antiferro-quadrupolar(AFQ) ordering and AFQ moments are coupled to the magnetic dipole and/or octupole moments.