Refractive index of biological specimens is a source of intrinsic contrast that can be explored without any concerns of photobleaching or harmful effects caused by extra contrast agents. In addition, RI contains rich information related to the metabolism of cells at the cellular and subcellular levels. Here, we report a no-moving parts approach that provides three-dimensional refractive index maps of biological samples continuously flowing in a microfluidic channel. Specifically, we use line illumination and off-axis digital holography to record the angular spectra of light scattered from flowing samples at high speed. Applying the scalar diffraction theory, we obtain accurate RI maps of the samples from the measured spectra. Using this method, we demonstrate label-free 3-D imaging of live RKO human colon cancer cells and RPMI8226 multiple myeloma cells, and obtain the volume, dry mass and density of these cells from the measured 3-D refractive index maps. Our results show that the reported method, alone or in combination with the existing flow cytometry techniques, promises as a quantitative tool for stain-free characterization of large number of cells.