One-minute rain rate exceeded for 0.01% of an average year (known as R0.01) is an important parameter, which is required in rain fade models for planning both satellite and terrestrial links, especially in the microwave and millimeter-wave bands. This paper presents the development of a new global model for estimating high-resolution R0.01. The model is developed using the Climate Hazards Group Infrared Precipitation with Stations (CHIRPS), ERA-Interim reanalyzed total precipitable water, and the cumulative distribution functions of the measured R0.01 via genetic algorithm. The newly proposed model performs better than the International Telecommunication Union Radio Sector (ITU-R) recommendation and widely used ITU-R P.837-6 model, particularly over the tropical regions, where ITU-R P.837-6 strongly underestimates R0.01. Overall, when compared to ITU-R P.837-6, the estimated R0.01 by the proposed model is improved by ~15%. Furthermore, the proposed model can provide R0.01 with a much higher spatial resolution (~5 km) as compared to ITU-R P.837-6 (~110 km). Another key advantage of the proposed model over ITU-R P.837-6 is that the inputs required for this model are readily available from meteorological database as well as from space-based observing system. This paper also investigated the long-term (1981–2016) trends in R0.01. The analysis revealed significant increasing trends in R0.01 over most parts of the globe, India and northern part of Southern America exhibited the strongest ( $\sim 0.5\,\,\text {mm}\cdot \text {h}^{-1}\cdot $ year−1) increasing trends. It is anticipated that R0.01 obtained with the newly proposed model will have large implications in rain attenuation modeling for planning both terrestrial and earth–satellite microwave links.