This paper reports a novel 3D topology optimization method based on the finite difference time domain (FDTD) method for a dielectric lens antenna. To obtain an optimal lens with smooth boundary, we apply normalized Gaussian networks (NGnet) to 3D topology optimization. Using the proposed method, the dielectric lens with desired radiation characteristics can be designed. As an example of the optimization using the proposed method, the width of the main beam is minimized assuming spatial symmetry. In the optimization, the lens is assumed to be loaded on the aperture of a waveguide slot antenna and is smaller compared with the wavelength. It is shown that the optimized lens has narrower beamwidth of the main beam than that of the conventional lens.