We present a reconstruction method for samples containing localized refractive index (RI) discontinuities in optical diffraction tomography. Abrupt RI changes induce regional phase perturbations and random spikes, which will be expanded and strengthened by existing tomographic algorithms, resulting in contaminated reconstructions. This method avoids the disturbance by recognition and separation of the discontinuous regions, and recombination of individually reconstructed data. Three-dimensional RI distributions of two fusion spliced optical fibers with different typical discontinuities are demonstrated, showing distinctly detailed structures of the samples as well as the positions and estimated shapes of the discontinuities.