In order to improve the application of neutron scattering technique, a new neutron optical device, which optical system consists of an array of several ten neutron Fresnel lenses, is designed by the researcher engaging in the study of neutron optics. Neutron Fresnel lenses for this new device have the same symmetric concave form. Its center is a spherical surface and the other surfaces are conic section. MgF2 single crystal glass is selected as the material for making neutron Fresnel lens because of its high transparence. Considering the form complicity and the brittle properties of MgF2 material, the fabrication of neutron Fresnel lens is of very difficulty. Form ELID (electrolytic in-process dressing) grinding was used for grinding the neutron Fresnel lens in this first study. The optima of grinding conditions for #325, #1200 and #4000 cobalt bonding diamond abrasive wheels are obtained through a series of tests. The MgF2 material is removed at the ductile mode by using #4000 abrasive wheel. Thus, the neutron Fresnel lens fabricated has low roughness and high transparence. The transmission of an array of 50 pieces of neutron Fresnel lens is 92.5 percents to neutron beam with wavelength 5Å and 79.3 percents to 16Å.