The simulation program AMPS-1D (analysis of microelectronic and photonic structures) employed to simulate and compare the performances of hydrogenated amorphous silicon germanium (a-SiGe:H) thin film solar cell with and without band gap grading at a radiation of AM1.5G (100 mW/cm2) and room temperature by introducing energy band engineering. The simulation results show that the efficiency of the solar cell with band gap grading is 0.477% higher than that without band gap grading due to the higher open circuit voltage (Voc) and better fill factor (FF). Subsequently, a-SiGe:H thin film solar cells with three different window layers such as hydrogenated amorphous silicon (a-Si:H), hydrogenated amorphous silicon carbide (a-SiC:H) and hydrogenated nanocrystalline silicon (nc-Si:H) are simulated, respectively. The numeric calculation results indicate that the fermi level EF of the a-SiGe:H thin film solar cell crosses the valence band when nc-Si:H window layer is employed in the simulation. This will improve the conductivity and the open circuit voltage of the solar cell. In addition, the electric field at front contact interface is reduced due to the lower contact barrier height. This may be more beneficial to the carrier collection by front contact. On the other hand, thanks to the wider band-gap difference between the window layer and the intrinsic layer, a potential barrier is built at the valence-band p/i interface due to the band offset. This will hinder the hole migration and collection. Thus, an nc-Si:H buffer layer, which can relax the valence-band offset and be more beneficial to the carrier migration and collection, is introduced at p/i interface. Finally, the optimum conversion efficiency of the a-SiGe:H thin film solar cell with graded band gap is achieved to be 9.104%.