In this article, a novel multi-beam leaky-wave antenna composed of a dualcomposite right-/left-handed meta-surface, including the defected ground structure contribution, is presented. The multi-mode operation of the antenna provides two different types of beams. The first, which is radiated from the meta-surface at the fundamental mode, is capable of continuous scanning from backward to forward angles. The second, which is radiated from the defected ground structure at the higher-order mode, is fixed at 59 ı . Operating principles are explained theoretically and experimentally. The measured radiation patterns demonstrate that the proposed antenna has two discrete scanning angles.