A tapered composite right/left-handed (CRLH) leaky-wave antenna (LWA) with reduced sidelobe level (SLL) is presented. A cosine taper design is achieved by simultaneously modifying the longitudinal period and the slot width of the mushroom CRLH structure. The design methodology is based on the use of parametric curves relating the phase and radiation constant of a single unit cell with diverse geometrical parameters. The radiation pattern results of the proposed structure show a significant SLL reduction in comparison with a non-tapered mushroom-like CRLH LWA, demonstrating the validity of the design methodology. © 2014 European Association on Antennas and Propagation.