© 2021 IEEE.We present design, simulation, and measurement of microwave beam generators that consist of dielectric rods. The structures are based on near-zero-index (NZI) properties of rod arrays when they are designed and arranged in specific configurations to induce near-zero permittivity and/or permeability in the host media. Once NZI properties are achieved, directive beams can be generated by relatively simple shell structures that sur-round isotropic sources. In order to obtain customized patterns, we further use lattice irregularities to suppress undesired beams on selected directions. In addition to extensive simulations of both homogenized and actual models, the effectiveness of the designs is verified by measurements on prototypes that are fabricated via 3D printing. The results demonstrate the feasibility of efficient beam generation with well-designed arrangements of dielectric rods, thanks to their interesting NZI characteristics.