Global solar radiation is the total sum of all radiations reaching the earth surface, i.e. it includes the direct and the diffused solar radiation reaching the earth surface. The instrument used for measuring this very important component arriving from the whole hemisphere is the pyranometer. This is one of the most important parameters for applications, developments, and researches related to the alternative source of clean and renewable energy. In cases where this data is not available, it is very common to use computational models to estimate the missing data, which is based mainly on the search for relationships between the weather variables such as temperature, humidity, precipitation, cloud cover, and sunshine hours, among others. In this research work, the baseline data for mean monthly global solar radiation (H) and sunshine hours (S) for three geopolitical zones of Nigeria (sub-sahara regions of Nigeria) with Sokoto (North-western Nigeria) (12.91(0)N, 5.20(0)E), Maiduguri (North-eastern Nigeria) (11.85(0)N, 13.08(0)E), and Ilorin (North-Central Nigeria) (8.43(0)N, 4.50(0)E) is obtained from the Nigeria Metrological Agency from 1996 to 2010. A linear regression correlation model is developed and the clearness index is estimated for each station. The results obtained show the angstrom coefficients a and b for estimating the global solar radiation for zone respectively using the angstrom-prescott model. The average global solar radiation for these stations is estimated, and the results obtained, subjected to statistical tests, are proven to be good estimates. It can be concluded that the Angstrom-Prescott model plays a significant role in predicting and estimating the solar energy potentials in these regions.