A numerical analysis of a photovoltaic-thermal (PVT) hybrid system with different cooling configurations is developed. The PVT system consists mainly of a photovoltaic panel and cooling fluid channels. The developed model is used to simulate the system PVT and to study the influence of different cooling patterns, operating and weather conditions on the system performance and to evaluate its energy and exergy efficiency. Five cooling patterns were tested: the first is cooled by air above the panel and water below the panel; the second is air cooling from above and below; the third is cooled by air above the panel only; the fourth is cooled by air below the panel only; and the fifth is cooled by water below the panel only. It was shown that the results of the developed model are consistent with the results of other published works. The performance of the PVT system was analyzed under the weather conditions of Sakaka Al-Jouf, KSA, in summer and winter. It was found that the best cooling pattern is the fifth and the worst is the second. The average panel temperature of (pattern 5) is 21 °C lower than the average panel temperature of pattern 2. The highest efficiency of total energy is 90% when water is used as coolant at the bottom of the panel and air at the top (pattern 1). The lowest efficiency of the total energy of the panel is 34% when the coolant is air at the bottom of the panel (pattern 4). The electrical energy efficiency, total energy efficiency, and total exergy efficiency are strongly influenced by the water flow rate and ambient temperature, while the effect of solar intensity is insignificant.