Optical diffraction tomography (ODT) provides three-dimensional refractive index (RI) tomograms of a transparent microscopic object. However, because of the finite numerical aperture of objective lenses, ODT has a limited access to diffracted light and suffers from poor spatial resolution, particularly along the axial direction. To overcome the limitation of the quality of RI tomography, we present an algorithm that accurately reconstructs RI tomography of a specimen with discrete and uniform RI, using prior information about the RI levels. Through simulations and experiments on various samples, including microspheres, red blood cells, and water droplets, we show that the proposed method can precisely reconstruct RI tomograms of samples which have discrete and homogenous RI distributions in the presence of the missing information and noise.