Annual rainfall maxima are commonly used for rainfall analysis, which entails the use of a distribution for modeling extreme values. Analysis of rainfall data from different regions of Texas, USA, shows that the form of the frequency distribution of annual rainfall maxima changes with different time durations, climate zones, and distances from the Gulf of Mexico. Employing the entropy theory, an entropy-based distribution for modeling annual rainfall maxima is derived, which is expected to apply across different time durations, climate zones, and distances from the Gulf. The performance of the proposed distribution is assessed with synthetic data from known distributions, and results show that the performance of the proposed entropy-based distribution is generally comparable with the generalized extreme value (GEV) distribution and is preferable for highly skewed data. Comparison based on observed rainfall data also shows this attractive property of the proposed distribution. Thus, the entropy-based distribution provides a promising alternative for frequency analysis of extreme rainfall values. The proposed distribution is then applied to the annual rainfall maxima, and results show that the entropy-based distribution fits the empirical probability distribution well and also performs well in modeling extreme rainfall values for different time durations, climate zones, and distances from the Gulf.