The 11B nuclear magnetic resonance in a dense Kondo system CeB6 has been observed by the spin echo technique below 4.2 K at fixed frequencies of 2.5, 6.5, 13.33 and 18.00 MHz, which correspond to magnetic fields of 1.83, 4.76, 9.76 and 13.18 KOe for the free 11B nucleus, respectively. The spectra in the phase II appeared to have two peaks in the magnetic field applied in the [111] direction, the spacing of which was found to be very small in zero external field and increased monotonically (up to 0.11 kOe at 2.6 K) with increasing field. On the other hand, the spectra in the phase III were complex. Especially, the spectra observed for [111] at 6.5 MHz were found to spread over 1.9 KOe and to have several peaks. From comparison between the experiments and the dipolar field calculation based on the recent neutron diffraction measurements, possible magnetic structures were examined for the phases II and III.