  We have measured optical reflectivity of Li and Ti doped NiO (LTNO) in the
infrared range at various temperatures. A Drude-like absorption is found at low
energy, $\omega <$ 100 cm$^{-1}$ and its spectral weight increases
substantially as temperature decreases. This observation and DC-resistivity
result show that LTNO has a conductive grain and resistive boundary. Such
composite structure provides evidence of the Maxwell-Wagner (MW) mechanism as
the origin of the high dielectric constant $\epsilon_{o}$. We propose a
three-phase granular structure and show that this extended MW model explains
the observed frequency and temperature dependence of the dielectric constant as
well as the giant value of $\epsilon_{o}$.
