Here, we present a novel microscopic technique for measuring wavelength-dependent three-dimensional (3-D) distributions of the refractive indices (RIs) of microscopic samples in the visible wavelengths. Employing 3-D quantitative phase microscopy techniques with a wavelength-swept source, 3-D RI tomograms were obtained in the range of 450 - 700 nm with a spectral resolution of a few nanometers. The capability of the technique was demonstrated by measuring the hyperspectral 3-D RI tomograms of polystyrene beads, human red blood cells, and hepatocytes. The results demonstrate the potential for label-free molecular specific 3-D tomography of biological samples.