This study examined the potential of narrow-bandgap (<1.1 eV) Cu(In,Ga)Se2 (CIGS) for use in monolithic perovskite/CIGS tandem solar cells, which have promising applications in flexible and lightweight photovoltaic systems. Single-graded (SG) and double-graded (DG) band profiles were developed for CIGS bottom cells. Their performance was compared both under 1 Sun condition and under red illumination, which is closer to the illumination condition for a bottom cell in the tandem configuration. While DG cells showed higher performance under 1 Sun, under filtered red light, SG cells exhibited superior performance due to a larger gain in fill factor, which was due to less FF loss originating from voltage-dependent photocurrent than DG CIGS. A careful bandgap matching between a perovskite top cell and an SG CIGS bottom cell led to a bandgap combination of 1.65 eV for the top cell and 1.04 eV for the bottom cell, resulting in a champion perovskite/SG CIGS tandem solar cell with an in-house power conversion efficiency of 25.1%.