Antennas with a cosecant-squared pattern play a significant role in air-surveillance radar systems. In this article, a cosecant-squared pattern leaky-wave antenna (LWA) is synthesized using a ridge waveguide. The LWA consists of periodic shunt slots located at the broad wall of a ridge waveguide. To obtain the desired cosecant-squared pattern, the attenuation and the phase constant must be controlled properly along the antenna length. To this end, the slots offset and the ridge profile are properly tapered along the antenna. This adjustment is performed through an optimization algorithm such as a genetic algorithm (GA) optimization. Through the proposed antenna configuration, a cosecant-squared pattern LWA with a wide range of 10° to 40° together with low ripples (≤2 dB) in the shaped region and a low level of sidelobes (≤−18 dB) is synthesized, fabricated and measured. Apart from the good agreement between the simulation and the measurement results, such a design indicates a size reduction (about 47%) compared with the previous published work.