Fixed-frequency beam scanning leaky-wave antennas (LWAs) that can scan their main beam over a specific frequency band are highly desired for future wireless communication systems. A composite right-/left-handed (CRLH) LWA is developed in this article that facilitates fixed-frequency continuous beam scanning over a wide operational frequency band. A variation of a simple single-layer nonreconfigurable frequency-based continuous beam scanning CRLH LWA is considered first. Its dispersion properties are approximately investigated using an equivalent circuit model. It is reported how two groups of varactor diodes can be incorporated into its basic circuit model to electronically control its dispersion behavior. An optimized reconfigurable CRLH LWA with practical dc biasing lines is then realized from this nonreconfigurable design. Fixed-frequency continuous beam scanning, from backward to forward directions through broadside, is reported over a wide operational frequency band. Simulations predict that the antenna can operate from 4.75 to 5.25 GHz with the main beam being continuously scannable at each frequency point. A prototype was fabricated, assembled, and tested. The measured results confirm its simulated performance characteristics.