The photovoltaic thermal system has a limitation in supplying hot water at the required temperature since it requires a supplementary heating system. One such system can be an air source heat pump operated by electricity from a PV/T system, which can be used to raise the temperature of the water preheated by PV/T to the required level. Such type system can also be called a hybrid PV/T-heat pump system, and it delivers thermal (hot water) and electrical energy. The performance of the hybrid PV/T-heat pump system was analyzed using the computational model for two Ethiopian cities, namely, Addis Ababa and Dire Dawa, which represent the highland and lowland regions, respectively. The simulation was conducted by inputting climatic data, daily hot water demand, and hourly hot water consumption patterns. Also, system design parameters such as PV/T area and peak Watt, PV/T warm water tank volume, air source heat pump water heater COP as a function of ambient temperature and circulating water temperature, and heat pump hot water tank volume. Besides, the effect of hot water consumption patterns (variability effect in three dissimilar cases constant, restaurant, and motel) on the system performance was examined. In addition, the effect of electric energy supply to the compressor of the heat pump using battery storage on the system performance was also investigated. In those diverse situations, the system in most of the cases generated hot water above 55°C and scored a COP of 3. The maximum value of hot water end-use efficiency of 66% was also obtained by making the hot water tank capacity about 50% of the daily hot water consumption size.