In this paper we present a theoretical investigation of an air based solar photovoltaic thermal (PVT) system integrated with phase change materials. The advantage of the air based PVT system is that the air can be directly used for space heating or cooling. At first we present an air based PVT system model and analyze the effect of major parameters on the system performance. We then integrate this PVT system model with a phase change material (PCM) energy storage system model and analyze the system performance. We found that solar irradiation increased thermal efficiency initially before reaching a plateau. However, electrical efficiency increases almost linearly with the solar irradiation. Increasing the air flow rate through the air channels, both the thermal and electrical efficiencies increase. Our results also showed that the channel depth has limited effect on the PVT system, only up to certain depth. The wind speed showed significant effect. As wind speed increases, the thermal efficiency decreases. This is due to the fact that with higher wind speed, much of the heat from the PVT surface (which is unglazed) is lost to the environment. This cools the PV plate and consequently increases its electrical efficiency. Our initial results also suggest that air based PVT system can supply considerable part of required space heating energy for a typical household. Incorporating PCM into PVT system enables the system to supplement heating, ventilation and air-conditioning energy demand even when the sun light or night cooling is not available.