This paper presents a new periodic grooved dielectric leaky-wave antenna (LWA) with non-identical irregularities for an extremely high-frequency (EHF) range capable of performing efficiently in the Ka band through a stable gain, a decrease in the level of the side lobes, and the achievement of a narrower main lobe beam. It consists of a dielectric waveguide antenna placed inside a channeled rectangular metallic waveguide to improve performance. A dielectric rod was used to overcome the losses related to the propagation of electromagnetic waves in metal conductors. A grooved dielectric of a 21-element linear array is used to propose a simple approach for the synthesis of such antennas based on a modified energy method and is fed by a standard waveguide. It was designed and simulated at 37.2 GHz for satellite, 5G antennas, and radar applications. The major novelty of this study is the ability to control the direction of the main lobe through non-identical irregularities in geometric parameters, such as the width, height, and distance between each element. Radiation techniques have been studied extensively using simulations. A performance antenna with radiation efficiency 99.35%, gain 22 dBi, width of radiation pattern 3.2 ◦ , and side lobe level (SLL) -18.3 dB has been achieved.