We propose low Rayleigh scattering Na2O-MgO-SiO2 (NMS) glass as a candidate material for low-loss optical fibers. This glass exhibits Rayleigh scattering which is only 0.4 times that of silica glass, and a theoretical evaluation suggests that it is dominated by density fluctuation. An investigation of the optical properties of NMS glass reveals that a minimum loss of 0.06 dB/km is expected at a wavelength of 1.6 µm and that the zero-material dispersion wavelength is found in the 1.5 µm band. To establish the waveguide structure, we evaluated the feasibility of using F-doped NMS (NMS-F) glass as a cladding layer for an NMS core and found that it is suitable because it exhibits low relative scattering (e.g. 0.7) and is versatile in terms of viscosity matching. We also describe an attempt to draw optical fibers using the double crucible technique.