The quasi-particle self-consistent GW (QSGW) method is a promising approach for investigating electronic structures, including excited states. However, its computational cost is relatively high compared to conventional electronic structure calculations based on the Kohn-Sham density functional theory (DFT). In this work, we introduce a highly powerful computational accelerator (GPU) to enhance the calculation speed, thereby expanding the applicability of the QSGW method. In this seminar, we review the fundamentals of the QSGW method, its implementation in computational codes, and the integration of GPU technology. By effectively utilizing GPUs, we achieved a significant reduction in computational time. As a demonstration of these advancements, we will present results for type-II semiconductor superlattices (InAs/GaSb) and ferromagnetic shape memory alloys (Ni2MnGa).