In the last years, the number of studies carried out in the field of acoustic metamaterials has significantly increased. In year 2009, our group proposed a concept of acoustic composite right/left hand transmission line (CRLH-TL) metamaterial, consisting of a waveguide periodically loaded with membranes along the duct, and transverse open channels (denoted “stubs”). It has then paved the way to antenna applications among which “Acoustic Leaky-Wave Antenna”. As, these antennas have very special properties such as frequency-dependant directivity, several practical applications are foreseen in the future. However, preliminary experimental work show that the low radiation efficiency of such axisymmetrical structures prevents its use in practice. To counteract this issue, an idea would consist in designing a similar structure, but with plane-symmetry rather than axial-symmetry. In this article, following our path on maturing the Acoustic Leaky-Wave antenna we propose an optimized design which unlike our previous structure is only radiating in the upper plane.