A composite right/left-handed (CRLH) leaky-wave antenna (LWA) can effectively scan the radiation beam from backward-to-forward direction. However, in most cases, a large range of frequency sweep is required to achieve a wide-angle beam scan, which could limit their applications. An in-depth study is conducted on an equivalent circuit model for a CRLH LWA unit cell to find the controlling parameters on the frequency sweeping range. A systematic design guideline is given for a CRLH LWA for a wide-angle beam scan in a flexibly chosen frequency range. It is shown that beam scanning by sweeping frequency in a target range can be achieved by systematically designing the unit cell parameters. To verify our approach, a novel CRLH unit cell is developed and used to design an LWA for a wide-angle beam scan in a narrow frequency range. Finally, the concept is validated through realization of the antenna and its measurement. The measured results show that the antenna prototype can scan its beam from -56° to +51° when frequency sweeps from 5.1 to 6.11 GHz (i.e., 18.02% of fractional bandwidth).